library(igraph)
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union

Cargamos el dataset

En primera medida, decidimos samplear el dataset de BuzzFeedNewsUser.txt, ya que la cantidad de nodos y links era demasiado grande para poder trabajar con el en nuestras computadoras. Este dataset cuenta con tres columnas: 1. El id de la noticia 2. El id del usuario 3. Cantidad de posteos/retweets del usuario sobre esa noticia.

Decidimos eliminar la columna del punto tres para simplificar el análisis. Si quisieramos profundizar el análisis, podríamos usar esta tercera columna como los pesos de la red bipartita.

BF_news_users <- read.csv("../DatosKaggle/BuzzFeed/sample/BuzzFeedNewsUser_newshash_20210815.csv", header=FALSE, encoding = "utf-8-sig")
BF_news_users <- BF_news_users[-1,]
BF_news_users$V1 = as.character(BF_news_users$V1)
g <- graph.data.frame(BF_news_users)

Utilizando bipartite.mapping podemos diferenciar a cada tipo de nodo. Esto requiere que inicialmente los tipos de datos que le pasemos a bipartite.mapping sean distintos. En este caso esto ya esta solucionado. Los ids de usuarios son numéricos, mientras que los ids de las noticias son un hash único creado en el procesamiento del dataset en el Jupyter Notebook.

bipartite.mapping(g)
## $res
## [1] TRUE
## 
## $type
##    [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [13] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [25] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [37] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##  [553] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [565] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [577] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##  [637] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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##  [889] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [1033] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [1045] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
## [1057]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
## [1069]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
## [1081]  TRUE  TRUE
V(g)$type <- bipartite_mapping(g)$type
V(g)$color <- ifelse(V(g)$type, "lightblue", "salmon")
V(g)$shape <- ifelse(V(g)$type, "circle", "square")
E(g)$color <- "lightgray"

plot(g, 
     vertex.label = NA, 
     vertex.size = 3,
     edge.arrow.size=0.1, 
     vertex.label.color = "black",
     layout=layout_components)

Los nodos cuadrados representan los usuarios y los nodos circulares celestes representan las noticias.

Creación de Redes

Utilizando bipartite_projection() creamos la red de usuarios-usuarios y de noticias-noticias

user-user: Red que representa el número de usuarios que cada noticia tiene en común

news-news: Red que representa el número de noticias que cada usuario tiene en común

projection_g <- bipartite_projection(g, multiplicity = TRUE)

users_projected <- projection_g$proj1
news_projected <- projection_g$proj2
V(news_projected)$color <- "lightblue"
V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = NA, 
     vertex.size = 3,
     edge.arrow.size=0.1, 
     vertex.label.color = "black",
     layout=layout_components)

V(users_projected)$color <- "salmon"
V(users_projected)$shape <- "square"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = NA, 
     vertex.size = 3,
     edge.arrow.size=0.1, 
     vertex.label.color = "black",
     layout=layout_components)

Análisis de las redes

Proyección: Red Noticias-Noticias

Análisis de los componentes de la red

connected_components = components(news_projected)

connected_components
## $membership
## A8E571 F466AA 9C8FAF B4EA27 229D27 F6430A 8B4AE4 7EB31E 6513A0 CA534D 19776E 
##      1      1      1      1      1      1      1      1      1      1      1 
## C2F13C 5C5CB8 232D46 3D02CC 5D1A52 8FFAFB 7E4715 A26558 92F413 3A6ED0 78D9FA 
##      1      1      1      1      1      1      1      1      1      1      1 
## 581460 633F13 535FB1 719576 C3D240 7253B0 A0E7B2 CCFD5A 3DBF7A 290C3D 57EF1C 
##      1      1      1      1      1      1      1      1      1      1      1 
## 577445 2C2ED2 AB6B13 24CE0B 
##      1      1      1      1 
## 
## $csize
## [1] 37
## 
## $no
## [1] 1
connected_components$no
## [1] 1
connected_components$csize
## [1] 37

Medidas de Centralidad Basadas en Primeros Vecinos

Degree Centrality

degree_centrality = degree(news_projected)

sort(degree_centrality)
## CA534D CCFD5A 2C2ED2 AB6B13 6513A0 3DBF7A 290C3D 57EF1C 24CE0B 7EB31E F466AA 
##      1      2      2      2      3      3      3      3      3      4      5 
## 7E4715 C3D240 577445 3D02CC 3A6ED0 7253B0 5D1A52 719576 19776E 78D9FA 633F13 
##      5      5      5      6      6      6      7      7      8      8      9 
## 8B4AE4 A0E7B2 9C8FAF 229D27 C2F13C 5C5CB8 F6430A 232D46 A26558 92F413 A8E571 
##     11     11     12     12     12     12     13     13     13     13     14 
## 8FFAFB 581460 535FB1 B4EA27 
##     14     14     15     18
max(degree_centrality)
## [1] 18

El nodo con mayor degree es B4EA27, el Cuál representa a la noticia, catalogada como real, con título: National poll: Clinton leads Trump by 6. Le siguen:

  • 535FB1: Barack Obama at Benjamin Netanyahu meeting: ‘He is always very candid with us’ (Real)
  • 581460: Sacramento mayor punches pie thrower (Real)
  • 8FFAFB: “Donald Trump: Drugs a ‘Very, Very Big Factor’ in Charlotte Protests” (Real)
  • A8E571: Federal Agents Make Massive Discovery at Southern Border… ISIS Is Here ⋆ Freedom Daily (Fake)
hist(unname(degree_centrality),labels = TRUE, xlim = c(0,18), ylim = c(0,8), xlab = "Degree", main = "Histograma de los Degree")

A continuación graficamos la proyección de la red bipartita en función de las noticias. Cada nodo tiene asignado un color que coincide con el degree del mismo:

colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
colors <- colorfunc(max(degree_centrality))
V(news_projected)$color <- colors[degree_centrality]
V(news_projected)$label <- degree_centrality
V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.size = 8,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Noticias: Nodos según el Degree")

El in-degree y out-degree es el mismo dado que la red no es dirigida.

Eigenvector Centrality

Esta métrica nos da una intuición de la influencia que un nodo tiene en la red. Si un nodo es alcanzado por muchos otros nodos (que además tienen una alta eigenvector centrality) ese nodo va a tener un eigenvector centrality mayor.

Podríamos decir que eigenvector centrality calcula el acceso indirecto al poder de un determinado nodo.

eigenvector_cetrality <- evcent(news_projected)$vector
eigenvector_cetrality
##       A8E571       F466AA       9C8FAF       B4EA27       229D27       F6430A 
## 4.747534e-03 3.104493e-02 7.315087e-01 1.000000e+00 3.018739e-01 6.599773e-01 
##       8B4AE4       7EB31E       6513A0       CA534D       19776E       C2F13C 
## 1.458165e-03 1.524449e-02 5.646678e-03 4.155654e-03 2.000607e-04 2.203432e-01 
##       5C5CB8       232D46       3D02CC       5D1A52       8FFAFB       7E4715 
## 5.724806e-01 3.123656e-01 8.137546e-04 1.082638e-03 8.102800e-01 4.118663e-03 
##       A26558       92F413       3A6ED0       78D9FA       581460       633F13 
## 2.825551e-01 7.730089e-01 3.997119e-03 3.575415e-04 3.261817e-01 1.670851e-04 
##       535FB1       719576       C3D240       7253B0       A0E7B2       CCFD5A 
## 2.168248e-01 1.000296e-04 1.262598e-05 3.376097e-05 2.025147e-01 1.515582e-02 
##       3DBF7A       290C3D       57EF1C       577445       2C2ED2       AB6B13 
## 9.548266e-05 9.548266e-05 2.670758e-02 5.611975e-02 5.851409e-02 1.286112e-04 
##       24CE0B 
## 1.246838e-04
hist(eigenvector_cetrality, labels = TRUE, ylim = c(0,30), xlab = "Eigenvector Centrality", main = "Histograma de los Valores de Eigenvector Centrality")

Según este histograma, hay dos nodos que tienen un eigenvector centrality mayor a 0.8. Veamos cuales son:

which(eigenvector_cetrality >=0.8)
## B4EA27 8FFAFB 
##      4     17
  • B4EA27: National poll: Clinton leads Trump by 6 (Real)
  • 8FFAFB: “Donald Trump: Drugs a ‘Very, Very Big Factor’ in Charlotte Protests” (Real)
colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
scaled_eigen = (eigenvector_cetrality * 10) +1
colors <- colorfunc(max(scaled_eigen))
V(news_projected)$color <- colors[scaled_eigen]
V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(eigenvector_cetrality, 2), nsmall = 1),
     vertex.size = 12,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Noticias: Nodos según el Eigenvector Centrality")

Pagerank Centrality

page_rank = page.rank(news_projected)$vector
page_rank
##      A8E571      F466AA      9C8FAF      B4EA27      229D27      F6430A 
## 0.083888781 0.008883901 0.045454404 0.089577439 0.028207245 0.046552555 
##      8B4AE4      7EB31E      6513A0      CA534D      19776E      C2F13C 
## 0.052409647 0.012176086 0.008384935 0.004746437 0.022851581 0.020549795 
##      5C5CB8      232D46      3D02CC      5D1A52      8FFAFB      7E4715 
## 0.040725333 0.025164500 0.038602081 0.046803996 0.051943193 0.028722855 
##      A26558      92F413      3A6ED0      78D9FA      581460      633F13 
## 0.030139016 0.048326124 0.025849669 0.026306999 0.033330557 0.018378688 
##      535FB1      719576      C3D240      7253B0      A0E7B2      CCFD5A 
## 0.026190228 0.017189248 0.012737391 0.014201158 0.017787098 0.008779622 
##      3DBF7A      290C3D      57EF1C      577445      2C2ED2      AB6B13 
## 0.013500548 0.013500548 0.007574367 0.006863394 0.007834791 0.006678291 
##      24CE0B 
## 0.009187501
hist(page_rank, labels = TRUE, ylim = c(0,10), xlim = c(0,0.1), xlab = "PageRank Centrality", main = "Histograma de los Valores de PageRank Centrality")

Según este histograma, hay dos noticias que poseen una centralidad relativamente alta. Veamos cuales son:

which(page_rank >= 0.08)
## A8E571 B4EA27 
##      1      4
  • A8E571: Federal Agents Make Massive Discovery at Southern Border… ISIS Is Here ⋆ Freedom Daily (Fake)
  • B4EA27: National poll: Clinton leads Trump by 6 (Real)

En el siguiente gáfico, graficamos la red y cada nodo tiene como label el page ranks score pero escalado, ya que es más fácil visualizar de esa forma.

colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
scaled_page_rank = (page_rank * 1000) 
colors <- colorfunc(max(scaled_page_rank))
V(news_projected)$color <- colors[scaled_page_rank]
V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(scaled_page_rank), nsmall = 1),
     vertex.size = 12,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Noticias: Nodos según Page Rank Score Escalado")

Authorities & Hubs

Authorities

authority = authority.score(news_projected)$vector
authority
##       A8E571       F466AA       9C8FAF       B4EA27       229D27       F6430A 
## 4.747534e-03 3.104493e-02 7.315087e-01 1.000000e+00 3.018739e-01 6.599773e-01 
##       8B4AE4       7EB31E       6513A0       CA534D       19776E       C2F13C 
## 1.458165e-03 1.524449e-02 5.646678e-03 4.155654e-03 2.000607e-04 2.203432e-01 
##       5C5CB8       232D46       3D02CC       5D1A52       8FFAFB       7E4715 
## 5.724806e-01 3.123656e-01 8.137546e-04 1.082638e-03 8.102800e-01 4.118663e-03 
##       A26558       92F413       3A6ED0       78D9FA       581460       633F13 
## 2.825551e-01 7.730089e-01 3.997119e-03 3.575415e-04 3.261817e-01 1.670851e-04 
##       535FB1       719576       C3D240       7253B0       A0E7B2       CCFD5A 
## 2.168248e-01 1.000296e-04 1.262598e-05 3.376097e-05 2.025147e-01 1.515582e-02 
##       3DBF7A       290C3D       57EF1C       577445       2C2ED2       AB6B13 
## 9.548266e-05 9.548266e-05 2.670758e-02 5.611975e-02 5.851409e-02 1.286112e-04 
##       24CE0B 
## 1.246838e-04
hist(authority, labels = TRUE, ylim = c(0,30), xlim = c(0,1), xlab = "Authority Score", main = "Histograma de los Valores de Authority Score")

según este histograma, hay dos noticias que poseen un authority relativamente alta. Veamos cuales son:

which(authority >= 0.8)
## B4EA27 8FFAFB 
##      4     17
  • B4EA27: National poll: Clinton leads Trump by 6 (Real)
  • A8E571: Federal Agents Make Massive Discovery at Southern Border… ISIS Is Here ⋆ Freedom Daily (Fake)
colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_authority = authority *1000000
colors <- colorfunc(max(scaled_authority))
V(news_projected)$color <- colors[scaled_authority]

V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(authority, 2), nsmall = 1),
     vertex.label.color = "Black",
     vertex.size = 14,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Noticias: Nodos según Authority Score")

Hubs

hubs = hub.score(news_projected)$vector
hubs
##       A8E571       F466AA       9C8FAF       B4EA27       229D27       F6430A 
## 4.747534e-03 3.104493e-02 7.315087e-01 1.000000e+00 3.018739e-01 6.599773e-01 
##       8B4AE4       7EB31E       6513A0       CA534D       19776E       C2F13C 
## 1.458165e-03 1.524449e-02 5.646678e-03 4.155654e-03 2.000607e-04 2.203432e-01 
##       5C5CB8       232D46       3D02CC       5D1A52       8FFAFB       7E4715 
## 5.724806e-01 3.123656e-01 8.137546e-04 1.082638e-03 8.102800e-01 4.118663e-03 
##       A26558       92F413       3A6ED0       78D9FA       581460       633F13 
## 2.825551e-01 7.730089e-01 3.997119e-03 3.575415e-04 3.261817e-01 1.670851e-04 
##       535FB1       719576       C3D240       7253B0       A0E7B2       CCFD5A 
## 2.168248e-01 1.000296e-04 1.262598e-05 3.376097e-05 2.025147e-01 1.515582e-02 
##       3DBF7A       290C3D       57EF1C       577445       2C2ED2       AB6B13 
## 9.548266e-05 9.548266e-05 2.670758e-02 5.611975e-02 5.851409e-02 1.286112e-04 
##       24CE0B 
## 1.246838e-04
hist(hubs, labels = TRUE, ylim = c(0,30), xlim = c(0,1), xlab = "Hub Score", main = "Histograma de los Valores de Hub Score")

Según este histograma, hay dos noticias que poseen un authority relativamente alta. Veamos cuales son:

which(hubs >= 0.8)
## B4EA27 8FFAFB 
##      4     17
  • B4EA27: National poll: Clinton leads Trump by 6 (Real)
  • A8E571: Federal Agents Make Massive Discovery at Southern Border… ISIS Is Here ⋆ Freedom Daily (Fake)
colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_hubs = hubs * 1000000
colors <- colorfunc(max(scaled_hubs))
V(news_projected)$color <- colors[scaled_hubs]

V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(hubs, 2), nsmall = 1),
     vertex.label.color = "Black",
     vertex.size = 14,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Noticias: Nodos según Hubs Score")

Medidas de Centralidad Basadas en Caminos más Cortos

Closeness Centrality

closeness_centrality = closeness(news_projected)
closeness_centrality
##      A8E571      F466AA      9C8FAF      B4EA27      229D27      F6430A 
## 0.012195122 0.008928571 0.009803922 0.010000000 0.008771930 0.010526316 
##      8B4AE4      7EB31E      6513A0      CA534D      19776E      C2F13C 
## 0.010416667 0.010204082 0.007692308 0.006711409 0.007874016 0.008849558 
##      5C5CB8      232D46      3D02CC      5D1A52      8FFAFB      7E4715 
## 0.010869565 0.010752688 0.007352941 0.007633588 0.010752688 0.010309278 
##      A26558      92F413      3A6ED0      78D9FA      581460      633F13 
## 0.008771930 0.010309278 0.011363636 0.007751938 0.009259259 0.010204082 
##      535FB1      719576      C3D240      7253B0      A0E7B2      CCFD5A 
## 0.012987013 0.009708738 0.007812500 0.008547009 0.009900990 0.007462687 
##      3DBF7A      290C3D      57EF1C      577445      2C2ED2      AB6B13 
## 0.008849558 0.008849558 0.008474576 0.008849558 0.005434783 0.009009009 
##      24CE0B 
## 0.008928571
hist(closeness_centrality, labels = TRUE, ylim = c(0,11), xlim = c(0.004,0.014), xlab = "Closeness Centrality", main = "Histograma de los Valores de Closeness Centrality")

Graficamos a continuación la red de noticias-noticias donde cada nodo tiene el tamaño y color asociado a la métrica de closeness calculada anteriormente.

colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_closeness = closeness_centrality * 1000
colors <- colorfunc(max(scaled_closeness))
V(news_projected)$color <- colors[scaled_closeness]

V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(closeness_centrality, 4), nsmall = 1),
     vertex.labe.color = "black",
     vertex.size =  closeness_centrality *1000 / 2,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Noticias: Nodos Según Closeness Centrality")

plot(news_projected, 
     vertex.label = NA,
     vertex.size =  closeness_centrality *1000 / 2,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Noticias: Nodos Según Closeness Centrality")

Betweenness Centrality

betweenness_centrality <- betweenness(news_projected)
betweenness_centrality
##      A8E571      F466AA      9C8FAF      B4EA27      229D27      F6430A 
## 176.4977723  24.4825002   7.4967341  81.0948007   8.7889510  13.5588993 
##      8B4AE4      7EB31E      6513A0      CA534D      19776E      C2F13C 
##  53.0275825  68.5657207   4.4201801   0.0000000   9.4333333   7.5729006 
##      5C5CB8      232D46      3D02CC      5D1A52      8FFAFB      7E4715 
##  25.5415037  35.9062866   2.1666667   0.0000000  46.3262140  32.4954885 
##      A26558      92F413      3A6ED0      78D9FA      581460      633F13 
##  38.0216783  13.3910672  61.6611451   0.0000000  47.8756363  85.4078453 
##      535FB1      719576      C3D240      7253B0      A0E7B2      CCFD5A 
## 257.8292203  38.6850840   0.9000000  10.4333333  21.0681627   0.0000000 
##      3DBF7A      290C3D      57EF1C      577445      2C2ED2      AB6B13 
##   0.3333333   0.3333333   9.8244106  17.1075313   0.0000000   0.8333333 
##      24CE0B 
##  25.5333333
hist(betweenness_centrality, bins= 20, labels = TRUE, ylim = c(0,40), xlim = c(0,300), xlab = "Betweenness Centrality", main = "Histograma de los Valores de Betweenness Centrality")
## Warning in plot.window(xlim, ylim, "", ...): "bins" is not a graphical parameter
## Warning in title(main = main, sub = sub, xlab = xlab, ylab = ylab, ...): "bins"
## is not a graphical parameter
## Warning in axis(1, ...): "bins" is not a graphical parameter
## Warning in axis(2, ...): "bins" is not a graphical parameter

which(betweenness_centrality >= 100)
## A8E571 535FB1 
##      1     25
  • A8E571: Federal Agents Make Massive Discovery at Southern Border… ISIS Is Here ⋆ Freedom Daily (Fake)
  • 535FB1: Barack Obama at Benjamin Netanyahu meeting: ‘He is always very candid with us’ (Real)

Graficamos a continuación la red de noticias-noticias donde cada nodo tiene el tamaño y color asociado a la métrica de betweenness calculada anteriormente.

colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_betweenness = betweenness_centrality + 1
colors <- colorfunc(max(scaled_betweenness))
V(news_projected)$color <- colors[scaled_betweenness]
V(news_projected)$shape <- "circle"
E(news_projected)$color <- "lightgray"

plot(news_projected, 
     vertex.label = format(round(betweenness_centrality), nsmall = 1),
     vertex.size =  betweenness_centrality / 9,
     edge.arrow.size=0.1,
     layout = layout_nicely,
     main = "Proyección Red Noticias: Nodos Según Betweenness Centrality")

plot(news_projected, 
     vertex.label = NA,
     vertex.size =  betweenness_centrality / 9,
     edge.arrow.size=0.1,
     layout = layout_nicely,
     main = "Proyección Red Noticias: Nodos Según Betweenness Centrality")

Medidas Sobre Conjuntos de Nodos

Cliques

Cálculo de la distribución de cliques:

count_max_cliques(news_projected)
## [1] 26

La red contiene 66 cliques.

¿Cuál es el tamaño de cada clique?

total_cliques = max_cliques(news_projected) 
cliques_sizes = unlist(lapply(total_cliques, length))
h = hist(cliques_sizes, 
         ylim=c(0,40),
         breaks = 5,
         xlab = "Tamaño de los cliques", 
         ylab = "Frecuencia", 
         main = "Distribución del tamaño de los cliques" ) 

text(h$mids,h$counts,labels=h$counts, adj=c(0.5, -0.5))

Graficamos el clique más grande

largestCliques <- largest_cliques(news_projected)

largestClique_1 = largestCliques[[1]]
g_induced = induced_subgraph(news_projected, largestClique_1)
V(g_induced)$color <- "lightblue"

plot(g_induced,
     vertex.label = NA,
     layout=layout_components,
     edge.arrow.size=0.05,
     vertex.size = 10,
     main = "Clique Más Grande")

Medidas Globales

Radio

Calculado obteniendo el mínimo valor de eccentricity

eccentricity_metric = eccentricity(news_projected)
min(eccentricity_metric)
## [1] 3

Diametro

diameter_metric = diameter(news_projected)
diameter_metric
## [1] 7

Average Path Length

avg_path_length = mean_distance(news_projected, directed=F)
avg_path_length
## [1] 2.358859

Transitivity

clustering_avg = transitivity(news_projected, type = "average")
clustering_avg
## [1] 0.7297252

Coeficiente de Reciprocidad

reciprocity(news_projected)
## [1] 1

Subredes

K-Core

La función coreness nos da una tabla indicando que core pertenece a cada nodo:

coreness(news_projected)
## A8E571 F466AA 9C8FAF B4EA27 229D27 F6430A 8B4AE4 7EB31E 6513A0 CA534D 19776E 
##      5      4     11     11     11     11      5      3      3      1      5 
## C2F13C 5C5CB8 232D46 3D02CC 5D1A52 8FFAFB 7E4715 A26558 92F413 3A6ED0 78D9FA 
##     11     10     11      5      5     11      5     11     11      5      5 
## 581460 633F13 535FB1 719576 C3D240 7253B0 A0E7B2 CCFD5A 3DBF7A 290C3D 57EF1C 
##     11      5     11      5      5      5     11      2      3      3      3 
## 577445 2C2ED2 AB6B13 24CE0B 
##      5      2      2      3

En este gráfico podemos observar la red noticia-noticia. Cada nodo tiene un atributo asignado que es el K-core obtenido mediante la función de coreness. Además, cada nodo tiene asociado un color en función del valor del k-core. Los nodos con valores más altos, son los que están más densamente conectados.

kcore <- coreness(news_projected)    # Extraemos k-cores
V(news_projected)$core <- kcore      # Agregamos los k-cores calculados como atributo de los nodos

colorfunc <- colorRampPalette(c( "Red 2",
                                 "lightcoral",
                                 "tomato", 
                                 "orange",
                                 "Cadet Blue 1",
                                 "Yellow 3",
                                 "gold", 
                                 "lightgreen",
                                 "Light Steel Blue 2",
                                 "Royal Blue 1",
                                 "Deep Sky Blue 1",
                                 "Slate Blue"))
colors <- colorfunc(max(kcore))
V(news_projected)$color <- colors[kcore]

plot(news_projected, 
     vertex.label = kcore,
     vertex.size = 15,
     layout = layout_components,
     main = " Nodos Según El core al que Pertenecen")

egog = make_ego_graph(news_projected, order=1)
k_g = egog[[1]]
degree_k_g = degree(k_g)

colorfunc <- colorRampPalette(c( "Red 2",
                                 "lightcoral",
                                 "tomato", 
                                 "orange",
                                 "Cadet Blue 1",
                                 "Yellow 3",
                                 "gold", 
                                 "lightgreen",
                                 "Light Steel Blue 2",
                                 "Royal Blue 1",
                                 "Deep Sky Blue 1",
                                 "Slate Blue"))
scaled_degree = degree_k_g + 1
colors <- colorfunc(max(scaled_degree))
V(k_g)$color <- colors[scaled_degree]


plot(k_g, 
     vertex.size = 12,
     vertex.label = degree_k_g,
     edge.arrow.size=0.3,
     layout = layout_components,
     main = "Subgrafo Inducido Usuario-Usuario: Nodos Según Degree")

rm(news_projected)

Proyección: Red Usuarios

Análisis de los componentes de la red

connected_components = components(users_projected)

connected_components
## $membership
##    10    11    41    51   114    67    78    82    85    98   107   128   132 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##   133   134   143   144   169   182   187   189   203   231   234   246   254 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##   257   258   281   306   345   349   354   376   393   398   448   456   466 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##   470   471   478   499   519   521   522   529   533   568   595   620   639 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##   648   656   657   679   697   743   771   796   822   837   838   840   841 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##   859   861   873   917   940   946   948   968   973   976   994  1000  1002 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  1024  1031  1032  1039  1055  1076  1102  1110  1138  1163  1172  1175  1209 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  1214  1218  1223  1224  1257  1258  1280  1307  1313  1329  1362  1412  1415 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  1416  1424  1429  1445  1462  1467  1481  1483  1494  1507  1544  1559  1596 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  1598  1639  1657  1660  1705  1709  1718  1739  1752  1760  1790  1826  1833 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  1849  1884  1898  1902  1924  1933  1984  1994  2001  2011  2019  2026  2042 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2063  2084  2129  2143  2149  2188  2192  2193  2199  2227  2250  2286  2293 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2316  2329  2330  2335  2349  2350  2377  2380  2388  2393  2405  2415  2426 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2427  2460  2462  2466  2471  2484  2491  2492  2502  2504  2516  2524  2526 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2527  2533  2542  2549  2557  2562  2582  2596  2601  2603  2623  2660  2663 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2701  2720  2730  2738  2795  2806  2811  2820  2835  2844  2846  2849  2861 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  2872  2876  2908  2920  2951  2961  2986  2987  3009  3020  3029  3051  3058 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3065  3066  3091  3103  3119  3134  3136  3137  3150  3152  3158  3167  3186 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3187  3200  3230  3260  3265  3278  3298  3314  3327  3345  3350  3356  3384 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3397  3401  3404  3408  3411  3443  3459  3461  3469  3491  3505  3516  3519 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3533  3549  3554  3557  3571  3577  3595  3596  3635  3648  3651  3723  3727 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3728  3733  3750  3752  3753  3790  3833  3845  3857  3873  3893  3940  3965 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  3987  3989  4010  4011  4014  4068  4070  4080  4081  4102  4124  4159  4214 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  4229  4243  4245  4273  4276  4303  4304  4310  4323  4350  4352  4369  4374 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  4384  4432  4461  4470  4472  4476  4489  4526  4536  4542  4550  4590  4600 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  4615  4633  4667  4705  4708  4730  4750  4751  4756  4760  4792  4800  4801 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  4820  4822  4823  4833  4843  4846  4862  4864  4875  4879  4890  4904  4910 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  4921  4930  4954  4964  4982  5014  5015  5044  5049  5055  5057  5072  5103 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5115  5120  5132  5136  5146  5179  5189  5223  5231  5251  5292  5293  5327 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5331  5342  5359  5423  5424  5438  5446  5453  5461  5466  5507  5508  5531 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5547  5552  5554  5556  5564  5579  5583  5597  5624  5666  5670  5688  5707 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5714  5726  5731  5771  5793  5846  5849  5867  5881  5886  5899  5901  5902 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5904  5905  5906  5911  5912  5918  5920  5939  5948  5962  5965  5973  5994 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  5996  5999  6003  6009  6018  6022  6054  6078  6085  6118  6121  6125  6134 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  6145  6163  6169  6173  6190  6202  6221  6223  6258  6322  6336  6345  6349 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  6350  6354  6367  6370  6373  6391  6404  6451  6472  6498  6505  6554  6563 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  6576  6591  6600  6630  6647  6679  6690  6695  6742  6757  6764  6784  6785 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  6815  6821  6857  6860  6869  6876  6880  6901  6914  6918  6920  6938  6939 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  6943  6946  6949  6955  6962  7026  7041  7048  7082  7103  7109  7116  7129 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  7137  7194  7202  7242  7261  7277  7295  7313  7316  7335  7337  7345  7352 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  7367  7373  7375  7392  7397  7398  7401  7430  7456  7458  7461  7472  7480 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  7482  7483  7508  7514  7564  7566  7569  7578  7619  7623  7624  7649  7697 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  7718  7731  7746  7756  7762  7765  7772  7779  7825  7830  7837  7850  7859 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  7862  7887  7890  7902  7904  7905  7941  7962  7964  7966  7983  8006  8015 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  8030  8077  8113  8123  8133  8134  8168  8174  8181  8183  8208  8220  8223 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  8253  8267  8293  8294  8309  8338  8342  8362  8365  8370  8373  8382  8393 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  8413  8426  8485  8542  8546  8566  8593  8609  8627  8663  8679  8708  8742 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  8746  8751  8761  8783  8787  8798  8825  8831  8850  8868  8878  8880  8894 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  8914  8931  8939  8953  8957  8992  8997  9015  9018  9025  9048  9061  9095 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  9098  9117  9129  9140  9163  9204  9210  9228  9229  9250  9253  9309  9310 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  9320  9341  9350  9355  9358  9373  9384  9407  9413  9424  9481  9486  9500 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  9553  9568  9570  9596  9607  9619  9641  9652  9659  9661  9664  9679  9682 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  9684  9714  9726  9763  9766  9782  9785  9792  9794  9809  9816  9834  9848 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
##  9851  9857  9877  9895  9905  9920 10003 10012 10054 10105 10110 10117 10118 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 10130 10155 10178 10201 10206 10209 10212 10241 10262 10270 10279 10290 10303 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 10364 10371 10386 10404 10423 10439 10449 10475 10480 10487 10500 10512 10516 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 10527 10544 10549 10568 10572 10582 10590 10638 10650 10694 10708 10724 10730 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 10736 10759 10771 10774 10776 10782 10802 10808 10836 10862 10874 10882 10886 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 10891 10906 10920 10929 10944 10952 10974 10995 11011 11025 11044 11073 11074 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 11123 11132 11142 11146 11156 11164 11171 11178 11217 11225 11234 11257 11296 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 11302 11305 11342 11352 11388 11390 11396 11417 11443 11456 11457 11461 11504 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 11527 11559 11560 11592 11606 11608 11642 11664 11671 11678 11700 11704 11707 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 11728 11729 11735 11753 11757 11818 11820 11839 11843 11859 11862 11887 11896 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 11935 11980 11988 12016 12030 12032 12049 12051 12075 12084 12091 12109 12114 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12117 12128 12147 12160 12166 12190 12216 12236 12283 12307 12335 12367 12372 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12376 12380 12382 12389 12395 12397 12408 12427 12439 12450 12452 12465 12468 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12490 12496 12522 12527 12528 12537 12546 12550 12552 12554 12561 12568 12570 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12579 12593 12607 12609 12622 12648 12705 12707 12739 12751 12761 12782 12799 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12804 12806 12816 12843 12887 12888 12894 12901 12906 12918 12933 12943 12948 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 12956 12964 12968 12980 12984 13000 13035 13052 13087 13092 13104 13111 13133 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 13136 13137 13138 13143 13150 13154 13159 13188 13252 13261 13263 13284 13335 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 13336 13341 13360 13396 13450 13469 13497 13540 13553 13565 13586 13602 13621 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 13635 13636 13647 13656 13660 13674 13675 13682 13690 13732 13737 13742 13753 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 13755 13761 13777 13778 13782 13784 13791 13807 13892 13916 13962 13967 13989 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14009 14035 14037 14060 14061 14064 14085 14095 14104 14110 14118 14119 14122 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14125 14135 14137 14158 14187 14203 14204 14210 14216 14221 14256 14305 14311 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14318 14321 14346 14358 14362 14368 14374 14403 14404 14414 14422 14435 14443 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14481 14543 14571 14581 14592 14609 14628 14633 14635 14664 14683 14692 14725 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14741 14743 14747 14751 14762 14780 14781 14787 14817 14819 14860 14895 14907 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 14925 14945 14947 14955 14963 15005 15024 15037 15096 15134 15143 15194 15196 
##     1     1     1     1     1     1     1     1     1     1     1     1     1 
## 15200 15217 15220 15242 15249 
##     1     1     1     1     1 
## 
## $csize
## [1] 1045
## 
## $no
## [1] 1
connected_components$no
## [1] 1
connected_components$csize
## [1] 1045

Medidas de Centralidad Basadas en Primeros Vecinos

Degree Centrality

degree_centrality = degree(users_projected)

sort(degree_centrality)
##  2820  3260  4350  5579  9018  9857 10475 14609    85  2806  2872  6918 11164 
##     2     2     2     2     2     2     2     2     3     3     3     3     3 
## 11461  1826  7762  2533  4352  6914  9607 13916  9782  9895 10118 14571 14781 
##     3     4     4     5     5     5     5     5     6     6     6     6     7 
##   133  1657  2861  4800  5461 10836 11073 12166 13263 14256   132   456   841 
##    11    11    11    11    11    11    11    11    11    11    12    12    12 
##  2582  4550  4823 10212 11457 13635   114   595  1362  3461  4080  5132  6202 
##    12    12    12    12    12    12    14    14    14    14    14    14    14 
##  6939  8627 12816 13469   128  1032  2063  2250  2557  4124  4461  4879  5103 
##    14    14    14    14    18    18    18    18    18    18    18    18    18 
##  7472  9714 10886 11396 12128 12372 14104 14683 14860   143   743   837  1055 
##    18    18    18    18    18    18    18    18    18    21    21    21    21 
##  2405  3134  6345  6647  6876  7277  7337 10708 11302 11456 11980 12439 12554 
##    21    21    21    21    21    21    21    21    21    21    21    21    21 
## 12761 13138 13565 13778 14064  4590   519  3845  6173  9320 11729 12739 14311 
##    21    21    21    21    21    24    25    25    25    25    25    25    25 
##    41   144  1429  1462  1598  5014  7564 11156 11171   471   948  2466  3137 
##    28    28    28    28    28    28    28    28    28    30    30    30    30 
##  5886  5905  6373  7295  8393  8783  8787  8957  9061  9481 10512 10771 11044 
##    30    30    30    30    30    30    30    30    30    30    30    30    30 
## 13150 13636  3356  3733  4374  4751  4756  4875  4964  5597  6145  7825  7862 
##    30    30    31    31    31    31    31    31    31    31    31    31    31 
##  8030  8708 10110 11388 11843 12051 12307 13737 14216 15242  1718  4930   376 
##    31    31    31    31    31    31    31    31    31    31    34    40    44 
##   648  1445  2377  2951  3965  4214  4245  4615  5251  5292  6600  7430  7962 
##    44    44    44    44    44    44    44    44    44    44    44    44    44 
##  8663  9309  9384 10516 10694 11443 12593 14947   838  1031  1483  2199  2460 
##    44    44    44    44    44    44    44    44    46    46    46    46    46 
##  3491  3987  4904  4954  4982  5359  5424  6022  6349  6857  7458  7746  7859 
##    46    46    46    46    46    46    46    46    46    46    46    46    46 
##  8168  8253  8914  8939  9413 10279 10724 11352 12117 12382 12622 12843 12918 
##    46    46    46    46    46    46    46    46    46    46    46    46    46 
## 13660 14443 14633 15196   393  2623  2701  2987  3103  3167  4011  4705  4862 
##    46    46    46    46    48    48    48    48    48    48    48    48    48 
##  5044  5939  5999  7116  7345  7397  7569  7830  8362  9163  9664  9851 10776 
##    48    48    48    48    48    48    48    48    48    48    48    48    48 
## 11123 11142 11753 12527 12943 14009   187   306   976  1258  2019  2516  2720 
##    48    48    48    48    48    48    52    52    52    52    52    52    52 
##  3136  3401  3549  4801  5564  6134  6169  6350  6690  7109  8181  8365  8679 
##    52    52    52    52    52    52    52    52    52    52    52    52    52 
##  9596  9766  9809  9920 10262 10952 11011 11504 12522 12546 12804 13586 14110 
##    52    52    52    52    52    52    52    52    52    52    52    52    52 
## 14158 14221 14895 15134 15200  1307   657  9358   182  1002  1313  1494  2349 
##    52    52    52    52    52    53    57    61    62    62    62    62    62 
##  2491  3020  3635  3753  7902  8174  8746  9048  9553  9652 10874 11592 12283 
##    62    62    62    62    62    62    62    62    62    62    62    62    62 
## 12389 12395 14061 14581  5136    78   246   697  1639  1739  1760  1884  2011 
##    62    62    62    62    64    67    67    67    67    67    67    67    67 
##  2335  2393  2524  2961  3404  3411  3577  3595  3940  5146  5189  5446  5899 
##    67    67    67    67    67    67    67    67    67    67    67    67    67 
##  5948  6336  7137  7649  7850  7890  9407  9570  9641  9792 10423 10480 10582 
##    67    67    67    67    67    67    67    67    67    67    67    67    67 
## 11178 11305 11678 11820 12468 13154 13284 13335 13497 13621 13656 13690 14118 
##    67    67    67    67    67    67    67    67    67    67    67    67    67 
## 14955 15220 14204 12933  6078  8370  9679 15217  8267    11   257   345   349 
##    67    67    68    70    72    72    72    72    75    81    81    81    81 
##   398   499   533   639   796   822   861   873   946  1790  1924  2001  2192 
##    81    81    81    81    81    81    81    81    81    81    81    81    81 
##  2330  2730  2738  3058  3278  3505  3857  3989  4276  4470  4542  4890  5331 
##    81    81    81    81    81    81    81    81    81    81    81    81    81 
##  5554  5731  5912  6221  6322  6354  6404  6563  6764  6901  7041  7313  7401 
##    81    81    81    81    81    81    81    81    81    81    81    81    81 
##  7456  7697  7964  8006  8413  8742  8850  8953  9373  9486  9500 10117 10782 
##    81    81    81    81    81    81    81    81    81    81    81    81    81 
## 11132 11527 11664 11818 11839 11862 12114 12160 12450 12452 12705 12751 12782 
##    81    81    81    81    81    81    81    81    81    81    81    81    81 
## 12964 13052 13137 13682 13791 14374 14481 14817    82   968  4068  3873  2526 
##    81    81    81    81    81    81    81    81    85    87    87    92    93 
##  5055  5507 11728   254  3727  8878 10891 14963  2663    51   203   231   478 
##    93    93    93   102   110   110   110   115   120   126   126   126   126 
##   521   529   859  1209  1415  1424  1481  1709  1752  1902  2293  2415  2504 
##   126   126   126   126   126   126   126   126   126   126   126   126   126 
##  2603  2876  2986  3469  3554  3596  3651  3728  3752  4304  4792  4820  4921 
##   126   126   126   126   126   126   126   126   126   126   126   126   126 
##  5453  5911  6125  6576  6955  7461  7566  7765  7837  7966  8133  8338  8373 
##   126   126   126   126   126   126   126   126   126   126   126   126   126 
##  8426  8566  8825  8894  8997  9253  9350 10449 10544 10568 10590 10882 10920 
##   126   126   126   126   126   126   126   126   126   126   126   126   126 
## 11074 11559 11859 12016 12049 12236 12380 12397 12490 12496 13111 13360 13602 
##   126   126   126   126   126   126   126   126   126   126   126   126   126 
## 13742 13782 14095 14203 14358 14635 14692 15194  5508 11608  9140  2188  2562 
##   126   126   126   126   126   126   126   126   129   129   134   135   135 
##  3397  8880  9250  1110  4843  6009 10178 12956  3152 10404 12561  8309 10054 
##   137   137   137   140   140   140   140   140   141   141   141   143   153 
## 11342  1559  7772 13136 15143  3187   522   771  1544  1898  5115  7373  7756 
##   153   157   157   157   157   163   169   169   169   169   169   169   169 
##  8609 13087  8134  9848  3158  2596  6054   940  5120 15005    10   107   169 
##   169   169   170   170   181   196   196   202   207   215   220   220   220 
##   234   656   973  1024  1039  1102  1138  1172  1214  1223  1257  1280  1329 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  1705  1933  1984  1994  2286  2388  2484  2492  2502  2549  2601  2908  2920 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  3051  3066  3230  3350  3533  3571  3723  3750  3790  3893  4102  4159  4303 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  4310  4472  4476  4536  4600  4708  4750  4822  4833  4846  5015  5179  5231 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  5293  5327  5547  5624  5666  5670  5688  5707  5793  5867  5881  5901  5902 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  5904  5918  5994  6003  6085  6190  6367  6370  6391  6472  6498  6679  6695 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  6785  6938  6943  6946  7194  7261  7316  7335  7352  7398  7482  7508  7578 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  7718  7731  7887  7905  7941  7983  8015  8077  8113  8183  8208  8293  8342 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  8382  8542  8761  8798  8831  8931  9095  9117  9228  9229  9424  9568  9619 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
##  9684  9816  9834  9905 10003 10012 10290 10303 10439 10487 10549 10572 10736 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
## 10808 10995 11025 11217 11296 11417 11560 11671 11896 12032 12075 12084 12190 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
## 12367 12376 12427 12550 12552 12568 12609 12648 12894 12980 13092 13104 13133 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
## 13159 13261 13341 13553 13755 13761 13784 13967 13989 14037 14060 14137 14187 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
## 14321 14362 14368 14403 14414 14725 14741 14747 14780 14819 14925 15024 15037 
##   220   220   220   220   220   220   220   220   220   220   220   220   220 
## 14346 10105 13540   568  2227  3519 14119 11887    67    98   189   281   354 
##   221   231   231   246   246   246   246   248   253   253   253   253   253 
##   448   470   620   840   917   994  1000  1076  1218  1224  1412  1416  1507 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  1596  1660  1849  2026  2084  2129  2143  2149  2193  2350  2380  2462  2471 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  2527  2542  2795  2811  2835  2844  2849  3029  3065  3091  3119  3150  3186 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  3298  3314  3327  3345  3384  3408  3443  3459  3557  3648  3833  4014  4070 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  4081  4229  4243  4273  4323  4369  4432  4526  4633  4667  4760  4864  4910 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  5057  5072  5223  5342  5423  5438  5531  5556  5583  5726  5771  5849  5906 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  5965  5973  6118  6121  6163  6223  6258  6451  6505  6554  6742  6757  6821 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  6860  6920  6949  7026  7048  7082  7103  7129  7202  7242  7367  7375  7392 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  7480  7514  7619  7623  7779  7904  8220  8223  8294  8485  8546  8593  8868 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##  9015  9025  9204  9210  9310  9341  9355  9661  9682  9785  9794  9877 10130 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 10155 10201 10209 10270 10371 10500 10527 10730 10759 10774 10802 10862 10906 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 10929 10944 11146 11225 11257 11390 11606 11642 11700 11704 11757 11935 11988 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 12030 12091 12408 12465 12528 12537 12570 12579 12607 12799 12806 12887 12888 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 12906 12968 12984 13035 13143 13188 13252 13336 13396 13450 13647 13674 13675 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 13732 13753 13807 13892 13962 14035 14085 14122 14125 14135 14210 14305 14318 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
## 14422 14435 14543 14592 14628 14664 14743 14751 14787 14907 14945 15096 15249 
##   253   253   253   253   253   253   253   253   253   253   253   253   253 
##   258  4489  5962  6591  6784  6962 10364   466  5552  8751  1163  6880 12901 
##   257   257   257   257   257   257   257   260   260   260   265   265   265 
## 10206  5466  7483 10650  4384  6018  7624 10386 10638   134   679  1175  1467 
##   268   269   275   276   277   277   277   279   280   284   284   284   284 
##  2316  2329  2660  2846  3009  4010  4730  5049  5714  5846  5920  6869  8123 
##   284   284   284   284   284   284   284   284   284   284   284   284   284 
##  8992 10974 11735 12147 12216 12335 12707 13000 14762  2042  3265  9659 12109 
##   284   284   284   284   284   284   284   284   284   292   305   305   306 
##  3200  9726  9763 12948 13777  9129 10241  1833  6630  9098 11707  3516  2426 
##   308   316   316   316   321   349   349   369   369   369   369   393   395 
##  6815 11234  2427  5996 14404 
##   402   427   428   432   476
max(degree_centrality)
## [1] 476
hist(unname(degree_centrality),labels = TRUE, xlim = c(0,600), ylim = c(0,350), xlab = "Degree", main = "Histograma de los Degree")

A continuación graficamos la proyección de la red bipartita en función de los usuarios. Cada nodo tiene asignado un color que coincide con el degree del mismo:

colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
colors <- colorfunc(max(degree_centrality))
V(users_projected)$color <- colors[degree_centrality]
V(users_projected)$label <- degree_centrality
V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.size = 2,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Usuarios: Nodos Según Degree")

plot(users_projected, 
     vertex.size = 4,
     vertex.label = NA,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Usuarios: Nodos Según Degree")

Eigenvector Centrality

Esta métrica nos da una intuición de la influencia que un nodo tiene en la red. Si un nodo es alcanzado por muchos otros nodos (que además tienen una alta eigenvector centrality) ese nodo va a tener un eigenvector centrality mayor.

Podríamos decir que eigenvector centrality calcula el acceso indirecto al poder de un determinado nodo.

eigenvector_cetrality <- evcent(users_projected)$vector
eigenvector_cetrality
##           10           11           41           51          114           67 
## 1.851816e-04 1.283902e-03 3.094893e-02 8.309411e-02 8.051461e-03 7.473835e-01 
##           78           82           85           98          107          128 
## 1.361263e-05 1.320908e-03 3.240013e-04 7.473835e-01 1.851816e-04 5.317688e-05 
##          132          133          134          143          144          169 
## 1.632376e-06 8.568722e-03 8.693217e-01 1.384216e-02 3.094893e-02 1.851816e-04 
##          182          187          189          203          231          234 
## 1.252681e-01 7.865246e-06 7.473835e-01 8.309411e-02 8.309411e-02 1.851816e-04 
##          246          254          257          258          281          306 
## 1.361263e-05 1.506834e-02 1.283902e-03 1.955626e-04 7.473835e-01 7.865246e-06 
##          345          349          354          376          393          398 
## 1.283902e-03 1.283902e-03 7.473835e-01 3.124682e-02 1.113006e-05 1.283902e-03 
##          448          456          466          470          471          478 
## 7.473835e-01 1.632376e-06 2.210498e-04 7.473835e-01 1.292210e-02 8.309411e-02 
##          499          519          521          522          529          533 
## 1.283902e-03 2.829945e-02 8.309411e-02 1.716172e-01 8.309411e-02 1.283902e-03 
##          568          595          620          639          648          656 
## 2.177740e-04 3.192423e-06 7.473835e-01 1.283902e-03 3.124682e-02 1.851816e-04 
##          657          679          697          743          771          796 
## 3.914832e-02 8.693217e-01 1.361263e-05 1.384216e-02 1.716172e-01 1.283902e-03 
##          822          837          838          840          841          859 
## 1.283902e-03 1.384216e-02 3.671491e-05 7.473835e-01 1.632376e-06 8.309411e-02 
##          861          873          917          940          946          948 
## 1.283902e-03 1.283902e-03 7.473835e-01 2.196020e-01 1.283902e-03 1.292210e-02 
##          968          973          976          994         1000         1002 
## 1.376629e-01 1.851816e-04 7.865246e-06 7.473835e-01 7.473835e-01 1.252681e-01 
##         1024         1031         1032         1039         1055         1076 
## 1.851816e-04 3.671491e-05 5.317688e-05 1.851816e-04 1.384216e-02 7.473835e-01 
##         1102         1110         1138         1163         1172         1175 
## 1.851816e-04 9.947152e-02 1.851816e-04 1.923103e-04 1.851816e-04 8.693217e-01 
##         1209         1214         1218         1223         1224         1257 
## 8.309411e-02 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 1.851816e-04 
##         1258         1280         1307         1313         1329         1362 
## 7.865246e-06 1.851816e-04 1.147608e-05 1.252681e-01 1.851816e-04 8.051461e-03 
##         1412         1415         1416         1424         1429         1445 
## 7.473835e-01 8.309411e-02 7.473835e-01 8.309411e-02 3.094893e-02 3.124682e-02 
##         1462         1467         1481         1483         1494         1507 
## 3.094893e-02 8.693217e-01 8.309411e-02 3.671491e-05 1.252681e-01 7.473835e-01 
##         1544         1559         1596         1598         1639         1657 
## 1.716172e-01 1.016310e-01 7.473835e-01 3.094893e-02 1.361263e-05 8.568722e-03 
##         1660         1705         1709         1718         1739         1752 
## 7.473835e-01 1.851816e-04 8.309411e-02 5.977311e-06 1.361263e-05 8.309411e-02 
##         1760         1790         1826         1833         1849         1884 
## 1.361263e-05 1.283902e-03 4.206519e-05 8.273087e-01 7.473835e-01 1.361263e-05 
##         1898         1902         1924         1933         1984         1994 
## 1.716172e-01 8.309411e-02 1.283902e-03 1.851816e-04 1.851816e-04 1.851816e-04 
##         2001         2011         2019         2026         2042         2063 
## 1.283902e-03 1.361263e-05 7.865246e-06 7.473835e-01 6.573193e-03 5.317688e-05 
##         2084         2129         2143         2149         2188         2192 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 9.183034e-02 1.283902e-03 
##         2193         2199         2227         2250         2286         2293 
## 7.473835e-01 3.671491e-05 2.177740e-04 5.317688e-05 1.851816e-04 8.309411e-02 
##         2316         2329         2330         2335         2349         2350 
## 8.693217e-01 8.693217e-01 1.283902e-03 1.361263e-05 1.252681e-01 7.473835e-01 
##         2377         2380         2388         2393         2405         2415 
## 3.124682e-02 7.473835e-01 1.851816e-04 1.361263e-05 1.384216e-02 8.309411e-02 
##         2426         2427         2460         2462         2466         2471 
## 9.484796e-01 9.216813e-01 3.671491e-05 7.473835e-01 1.292210e-02 7.473835e-01 
##         2484         2491         2492         2502         2504         2516 
## 1.851816e-04 1.252681e-01 1.851816e-04 1.851816e-04 8.309411e-02 7.865246e-06 
##         2524         2526         2527         2533         2542         2549 
## 1.361263e-05 1.892283e-05 7.473835e-01 3.899759e-07 7.473835e-01 1.851816e-04 
##         2557         2562         2582         2596         2601         2603 
## 5.317688e-05 9.183034e-02 1.632376e-06 2.205150e-01 1.851816e-04 8.309411e-02 
##         2623         2660         2663         2701         2720         2730 
## 1.113006e-05 8.693217e-01 1.951956e-01 1.113006e-05 7.865246e-06 1.283902e-03 
##         2738         2795         2806         2811         2820         2835 
## 1.283902e-03 7.473835e-01 6.423139e-04 7.473835e-01 1.534919e-06 7.473835e-01 
##         2844         2846         2849         2861         2872         2876 
## 7.473835e-01 8.693217e-01 7.473835e-01 8.568722e-03 4.415451e-04 8.309411e-02 
##         2908         2920         2951         2961         2986         2987 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.361263e-05 8.309411e-02 1.113006e-05 
##         3009         3020         3029         3051         3058         3065 
## 8.693217e-01 1.252681e-01 7.473835e-01 1.851816e-04 1.283902e-03 7.473835e-01 
##         3066         3091         3103         3119         3134         3136 
## 1.851816e-04 7.473835e-01 1.113006e-05 7.473835e-01 1.384216e-02 7.865246e-06 
##         3137         3150         3152         3158         3167         3186 
## 1.292210e-02 7.473835e-01 8.318815e-05 2.075671e-01 1.113006e-05 7.473835e-01 
##         3187         3200         3230         3260         3265         3278 
## 1.441853e-01 8.788411e-01 1.851816e-04 3.859943e-03 8.967309e-01 1.283902e-03 
##         3298         3314         3327         3345         3350         3356 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 3.342656e-05 
##         3384         3397         3401         3404         3408         3411 
## 7.473835e-01 9.679743e-02 7.865246e-06 1.361263e-05 7.473835e-01 1.361263e-05 
##         3443         3459         3461         3469         3491         3505 
## 7.473835e-01 7.473835e-01 3.192423e-06 8.309411e-02 3.671491e-05 1.283902e-03 
##         3516         3519         3533         3549         3554         3557 
## 8.551731e-01 2.177740e-04 1.851816e-04 7.865246e-06 8.309411e-02 7.473835e-01 
##         3571         3577         3595         3596         3635         3648 
## 1.851816e-04 1.361263e-05 1.361263e-05 8.309411e-02 1.252681e-01 7.473835e-01 
##         3651         3723         3727         3728         3733         3750 
## 8.309411e-02 1.851816e-04 2.464828e-05 8.309411e-02 3.342656e-05 1.851816e-04 
##         3752         3753         3790         3833         3845         3857 
## 8.309411e-02 1.252681e-01 1.851816e-04 7.473835e-01 2.829945e-02 1.283902e-03 
##         3873         3893         3940         3965         3987         3989 
## 9.815029e-03 1.851816e-04 1.361263e-05 3.124682e-02 3.671491e-05 1.283902e-03 
##         4010         4011         4014         4068         4070         4080 
## 8.693217e-01 1.113006e-05 7.473835e-01 1.376629e-01 7.473835e-01 3.192423e-06 
##         4081         4102         4124         4159         4214         4229 
## 7.473835e-01 1.851816e-04 5.317688e-05 1.851816e-04 3.124682e-02 7.473835e-01 
##         4243         4245         4273         4276         4303         4304 
## 7.473835e-01 3.124682e-02 7.473835e-01 1.283902e-03 1.851816e-04 8.309411e-02 
##         4310         4323         4350         4352         4369         4374 
## 1.851816e-04 7.473835e-01 3.859943e-03 3.899759e-07 7.473835e-01 3.342656e-05 
##         4384         4432         4461         4470         4472         4476 
## 1.980357e-04 7.473835e-01 5.317688e-05 1.283902e-03 1.851816e-04 1.851816e-04 
##         4489         4526         4536         4542         4550         4590 
## 1.955626e-04 7.473835e-01 1.851816e-04 1.283902e-03 1.632376e-06 1.012641e-02 
##         4600         4615         4633         4667         4705         4708 
## 1.851816e-04 3.124682e-02 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 
##         4730         4750         4751         4756         4760         4792 
## 8.693217e-01 1.851816e-04 3.342656e-05 3.342656e-05 7.473835e-01 8.309411e-02 
##         4800         4801         4820         4822         4823         4833 
## 6.393403e-03 7.865246e-06 8.309411e-02 1.851816e-04 1.632376e-06 1.851816e-04 
##         4843         4846         4862         4864         4875         4879 
## 9.947152e-02 1.851816e-04 1.113006e-05 7.473835e-01 3.342656e-05 5.317688e-05 
##         4890         4904         4910         4921         4930         4954 
## 1.283902e-03 3.671491e-05 7.473835e-01 8.309411e-02 2.089353e-02 3.671491e-05 
##         4964         4982         5014         5015         5044         5049 
## 3.342656e-05 3.671491e-05 3.094893e-02 1.851816e-04 1.113006e-05 8.693217e-01 
##         5055         5057         5072         5103         5115         5120 
## 1.892283e-05 7.473835e-01 7.473835e-01 5.317688e-05 1.716172e-01 8.405604e-02 
##         5132         5136         5146         5179         5189         5223 
## 3.192423e-06 8.980721e-02 1.361263e-05 1.851816e-04 1.361263e-05 7.473835e-01 
##         5231         5251         5292         5293         5327         5331 
## 1.851816e-04 3.124682e-02 3.124682e-02 1.851816e-04 1.851816e-04 1.283902e-03 
##         5342         5359         5423         5424         5438         5446 
## 7.473835e-01 3.671491e-05 7.473835e-01 3.671491e-05 7.473835e-01 1.361263e-05 
##         5453         5461         5466         5507         5508         5531 
## 8.309411e-02 6.393403e-03 1.964649e-04 1.892283e-05 8.385015e-02 7.473835e-01 
##         5547         5552         5554         5556         5564         5579 
## 1.851816e-04 2.210498e-04 1.283902e-03 7.473835e-01 7.865246e-06 8.406202e-07 
##         5583         5597         5624         5666         5670         5688 
## 7.473835e-01 3.342656e-05 1.851816e-04 1.851816e-04 1.851816e-04 1.851816e-04 
##         5707         5714         5726         5731         5771         5793 
## 1.851816e-04 8.693217e-01 7.473835e-01 1.283902e-03 7.473835e-01 1.851816e-04 
##         5846         5849         5867         5881         5886         5899 
## 8.693217e-01 7.473835e-01 1.851816e-04 1.851816e-04 1.292210e-02 1.361263e-05 
##         5901         5902         5904         5905         5906         5911 
## 1.851816e-04 1.851816e-04 1.851816e-04 1.292210e-02 7.473835e-01 8.309411e-02 
##         5912         5918         5920         5939         5948         5962 
## 1.283902e-03 1.851816e-04 8.693217e-01 1.113006e-05 1.361263e-05 1.955626e-04 
##         5965         5973         5994         5996         5999         6003 
## 7.473835e-01 7.473835e-01 1.851816e-04 9.221897e-01 1.113006e-05 1.851816e-04 
##         6009         6018         6022         6054         6078         6085 
## 9.947152e-02 1.980357e-04 3.671491e-05 1.994648e-01 6.987382e-05 1.851816e-04 
##         6118         6121         6125         6134         6145         6163 
## 7.473835e-01 7.473835e-01 8.309411e-02 7.865246e-06 3.342656e-05 7.473835e-01 
##         6169         6173         6190         6202         6221         6223 
## 7.865246e-06 2.829945e-02 1.851816e-04 3.192423e-06 1.283902e-03 7.473835e-01 
##         6258         6322         6336         6345         6349         6350 
## 7.473835e-01 1.283902e-03 1.361263e-05 9.087979e-03 3.671491e-05 7.865246e-06 
##         6354         6367         6370         6373         6391         6404 
## 1.283902e-03 1.851816e-04 1.851816e-04 1.292210e-02 1.851816e-04 1.283902e-03 
##         6451         6472         6498         6505         6554         6563 
## 7.473835e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 
##         6576         6591         6600         6630         6647         6679 
## 8.309411e-02 1.955626e-04 3.124682e-02 8.273087e-01 9.087979e-03 1.851816e-04 
##         6690         6695         6742         6757         6764         6784 
## 7.865246e-06 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 1.955626e-04 
##         6785         6815         6821         6857         6860         6869 
## 1.851816e-04 9.728658e-01 7.473835e-01 3.671491e-05 7.473835e-01 8.693217e-01 
##         6876         6880         6901         6914         6918         6920 
## 9.087979e-03 1.923103e-04 1.283902e-03 1.077222e-03 7.570669e-08 7.473835e-01 
##         6938         6939         6943         6946         6949         6955 
## 1.851816e-04 8.051461e-03 1.851816e-04 1.851816e-04 7.473835e-01 8.309411e-02 
##         6962         7026         7041         7048         7082         7103 
## 1.955626e-04 7.473835e-01 1.283902e-03 7.473835e-01 7.473835e-01 7.473835e-01 
##         7109         7116         7129         7137         7194         7202 
## 7.865246e-06 1.113006e-05 7.473835e-01 1.361263e-05 1.851816e-04 7.473835e-01 
##         7242         7261         7277         7295         7313         7316 
## 7.473835e-01 1.851816e-04 9.087979e-03 1.292210e-02 1.283902e-03 1.851816e-04 
##         7335         7337         7345         7352         7367         7373 
## 1.851816e-04 1.384216e-02 1.113006e-05 1.851816e-04 7.473835e-01 1.716172e-01 
##         7375         7392         7397         7398         7401         7430 
## 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 1.283902e-03 3.124682e-02 
##         7456         7458         7461         7472         7480         7482 
## 1.283902e-03 3.671491e-05 8.309411e-02 5.317688e-05 7.473835e-01 1.851816e-04 
##         7483         7508         7514         7564         7566         7569 
## 1.947474e-04 1.851816e-04 7.473835e-01 3.094893e-02 8.309411e-02 1.292577e-02 
##         7578         7619         7623         7624         7649         7697 
## 1.851816e-04 7.473835e-01 7.473835e-01 1.980357e-04 1.361263e-05 1.283902e-03 
##         7718         7731         7746         7756         7762         7765 
## 1.851816e-04 1.851816e-04 3.671491e-05 1.716172e-01 4.206519e-05 8.309411e-02 
##         7772         7779         7825         7830         7837         7850 
## 1.415560e-01 7.473835e-01 3.342656e-05 1.113006e-05 8.309411e-02 1.361263e-05 
##         7859         7862         7887         7890         7902         7904 
## 3.671491e-05 3.342656e-05 1.851816e-04 1.361263e-05 1.252681e-01 7.473835e-01 
##         7905         7941         7962         7964         7966         7983 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.283902e-03 8.309411e-02 1.851816e-04 
##         8006         8015         8030         8077         8113         8123 
## 1.283902e-03 1.851816e-04 3.342656e-05 1.851816e-04 1.851816e-04 8.693217e-01 
##         8133         8134         8168         8174         8181         8183 
## 8.309411e-02 1.177450e-01 3.671491e-05 1.252681e-01 7.865246e-06 1.851816e-04 
##         8208         8220         8223         8253         8267         8293 
## 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.259357e-05 1.851816e-04 
##         8294         8309         8338         8342         8362         8365 
## 7.473835e-01 1.260691e-01 8.309411e-02 1.851816e-04 1.113006e-05 7.865246e-06 
##         8370         8373         8382         8393         8413         8426 
## 6.987382e-05 8.309411e-02 1.851816e-04 1.292210e-02 1.283902e-03 8.309411e-02 
##         8485         8542         8546         8566         8593         8609 
## 7.473835e-01 1.851816e-04 7.473835e-01 8.309411e-02 7.473835e-01 1.716172e-01 
##         8627         8663         8679         8708         8742         8746 
## 3.192423e-06 3.124682e-02 7.865246e-06 3.342656e-05 1.283902e-03 1.252681e-01 
##         8751         8761         8783         8787         8798         8825 
## 2.210498e-04 1.851816e-04 1.292210e-02 1.292210e-02 1.851816e-04 8.309411e-02 
##         8831         8850         8868         8878         8880         8894 
## 1.851816e-04 1.283902e-03 7.473835e-01 2.464828e-05 9.255031e-02 8.309411e-02 
##         8914         8931         8939         8953         8957         8992 
## 3.671491e-05 1.851816e-04 3.671491e-05 1.283902e-03 1.292210e-02 8.693217e-01 
##         8997         9015         9018         9025         9048         9061 
## 8.309411e-02 7.473835e-01 1.534919e-06 7.473835e-01 1.252681e-01 1.292210e-02 
##         9095         9098         9117         9129         9140         9163 
## 1.851816e-04 8.273087e-01 1.851816e-04 2.153154e-04 9.131307e-02 1.113006e-05 
##         9204         9210         9228         9229         9250         9253 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.851816e-04 9.255031e-02 8.309411e-02 
##         9309         9310         9320         9341         9350         9355 
## 3.124682e-02 7.473835e-01 2.829945e-02 7.473835e-01 8.309411e-02 7.473835e-01 
##         9358         9373         9384         9407         9413         9424 
## 1.426783e-05 1.283902e-03 3.124682e-02 1.361263e-05 3.671491e-05 1.851816e-04 
##         9481         9486         9500         9553         9568         9570 
## 1.292210e-02 1.283902e-03 1.283902e-03 1.252681e-01 1.851816e-04 1.361263e-05 
##         9596         9607         9619         9641         9652         9659 
## 7.865246e-06 3.899759e-07 1.851816e-04 1.361263e-05 1.252681e-01 8.967309e-01 
##         9661         9664         9679         9682         9684         9714 
## 7.473835e-01 1.113006e-05 6.987382e-05 7.473835e-01 1.851816e-04 5.317688e-05 
##         9726         9763         9766         9782         9785         9792 
## 2.337187e-04 2.337187e-04 7.865246e-06 8.048715e-03 7.473835e-01 1.361263e-05 
##         9794         9809         9816         9834         9848         9851 
## 7.473835e-01 7.865246e-06 1.851816e-04 1.851816e-04 1.177450e-01 1.113006e-05 
##         9857         9877         9895         9905         9920        10003 
## 8.441843e-07 7.473835e-01 8.048715e-03 1.851816e-04 7.865246e-06 1.851816e-04 
##        10012        10054        10105        10110        10117        10118 
## 1.851816e-04 1.139098e-01 1.876553e-04 3.342656e-05 1.283902e-03 8.048715e-03 
##        10130        10155        10178        10201        10206        10209 
## 7.473835e-01 7.473835e-01 9.947152e-02 7.473835e-01 1.964392e-04 7.473835e-01 
##        10212        10241        10262        10270        10279        10290 
## 1.632376e-06 2.153154e-04 7.865246e-06 7.473835e-01 3.671491e-05 1.851816e-04 
##        10303        10364        10371        10386        10404        10423 
## 1.851816e-04 1.955626e-04 7.473835e-01 1.980591e-04 9.656638e-02 1.361263e-05 
##        10439        10449        10475        10480        10487        10500 
## 1.851816e-04 8.309411e-02 7.784107e-07 1.361263e-05 1.851816e-04 7.473835e-01 
##        10512        10516        10527        10544        10549        10568 
## 1.292210e-02 3.124682e-02 7.473835e-01 8.309411e-02 1.851816e-04 8.309411e-02 
##        10572        10582        10590        10638        10650        10694 
## 1.851816e-04 1.361263e-05 8.309411e-02 5.188210e-04 7.753625e-01 3.124682e-02 
##        10708        10724        10730        10736        10759        10771 
## 1.384216e-02 3.671491e-05 7.473835e-01 1.851816e-04 7.473835e-01 1.292210e-02 
##        10774        10776        10782        10802        10808        10836 
## 7.473835e-01 1.113006e-05 1.283902e-03 7.473835e-01 1.851816e-04 8.568722e-03 
##        10862        10874        10882        10886        10891        10906 
## 7.473835e-01 1.252681e-01 8.309411e-02 5.317688e-05 2.464828e-05 7.473835e-01 
##        10920        10929        10944        10952        10974        10995 
## 8.309411e-02 7.473835e-01 7.473835e-01 7.865246e-06 8.693217e-01 1.851816e-04 
##        11011        11025        11044        11073        11074        11123 
## 7.865246e-06 1.851816e-04 1.292210e-02 6.393403e-03 8.309411e-02 1.113006e-05 
##        11132        11142        11146        11156        11164        11171 
## 1.283902e-03 1.113006e-05 7.473835e-01 3.094893e-02 4.415451e-04 3.094893e-02 
##        11178        11217        11225        11234        11257        11296 
## 1.361263e-05 1.851816e-04 7.473835e-01 1.000000e+00 7.473835e-01 1.851816e-04 
##        11302        11305        11342        11352        11388        11390 
## 1.384216e-02 1.361263e-05 3.236004e-05 3.671491e-05 3.342656e-05 7.473835e-01 
##        11396        11417        11443        11456        11457        11461 
## 5.317688e-05 1.851816e-04 3.124682e-02 9.087979e-03 1.632376e-06 7.570669e-08 
##        11504        11527        11559        11560        11592        11606 
## 7.865246e-06 1.283902e-03 8.309411e-02 1.851816e-04 1.252681e-01 7.473835e-01 
##        11608        11642        11664        11671        11678        11700 
## 8.310226e-02 7.473835e-01 1.283902e-03 1.851816e-04 1.361263e-05 7.473835e-01 
##        11704        11707        11728        11729        11735        11753 
## 7.473835e-01 8.273087e-01 1.892283e-05 2.829945e-02 8.693217e-01 1.113006e-05 
##        11757        11818        11820        11839        11843        11859 
## 7.473835e-01 1.283902e-03 1.361263e-05 1.283902e-03 3.342656e-05 8.309411e-02 
##        11862        11887        11896        11935        11980        11988 
## 1.283902e-03 2.177805e-04 1.851816e-04 7.473835e-01 1.384216e-02 7.473835e-01 
##        12016        12030        12032        12049        12051        12075 
## 8.309411e-02 7.473835e-01 1.851816e-04 8.309411e-02 3.342656e-05 1.851816e-04 
##        12084        12091        12109        12114        12117        12128 
## 1.851816e-04 7.473835e-01 2.050135e-04 1.283902e-03 3.671491e-05 5.317688e-05 
##        12147        12160        12166        12190        12216        12236 
## 8.693217e-01 1.283902e-03 8.568722e-03 1.851816e-04 8.693217e-01 8.309411e-02 
##        12283        12307        12335        12367        12372        12376 
## 1.252681e-01 3.342656e-05 8.693217e-01 1.851816e-04 5.317688e-05 1.851816e-04 
##        12380        12382        12389        12395        12397        12408 
## 8.309411e-02 3.671491e-05 1.252681e-01 1.252681e-01 8.309411e-02 7.473835e-01 
##        12427        12439        12450        12452        12465        12468 
## 1.851816e-04 9.087979e-03 1.283902e-03 1.283902e-03 7.473835e-01 1.361263e-05 
##        12490        12496        12522        12527        12528        12537 
## 8.309411e-02 8.309411e-02 7.865246e-06 1.113006e-05 7.473835e-01 7.473835e-01 
##        12546        12550        12552        12554        12561        12568 
## 7.865246e-06 1.851816e-04 1.851816e-04 1.384216e-02 9.656638e-02 1.851816e-04 
##        12570        12579        12593        12607        12609        12622 
## 7.473835e-01 7.473835e-01 3.124682e-02 7.473835e-01 1.851816e-04 3.671491e-05 
##        12648        12705        12707        12739        12751        12761 
## 1.851816e-04 1.283902e-03 8.693217e-01 2.829945e-02 1.283902e-03 1.490503e-02 
##        12782        12799        12804        12806        12816        12843 
## 1.283902e-03 7.473835e-01 7.865246e-06 7.473835e-01 3.192423e-06 3.671491e-05 
##        12887        12888        12894        12901        12906        12918 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.923103e-04 7.473835e-01 3.671491e-05 
##        12933        12943        12948        12956        12964        12968 
## 1.363611e-05 1.113006e-05 2.337187e-04 9.947152e-02 1.283902e-03 7.473835e-01 
##        12980        12984        13000        13035        13052        13087 
## 1.851816e-04 7.473835e-01 8.693217e-01 7.473835e-01 1.283902e-03 1.716172e-01 
##        13092        13104        13111        13133        13136        13137 
## 1.851816e-04 1.851816e-04 8.309411e-02 1.851816e-04 1.415560e-01 1.283902e-03 
##        13138        13143        13150        13154        13159        13188 
## 1.384216e-02 7.473835e-01 1.292210e-02 1.361263e-05 1.851816e-04 7.473835e-01 
##        13252        13261        13263        13284        13335        13336 
## 7.473835e-01 1.851816e-04 6.393403e-03 1.361263e-05 1.361263e-05 7.473835e-01 
##        13341        13360        13396        13450        13469        13497 
## 1.851816e-04 8.309411e-02 7.473835e-01 7.473835e-01 3.192423e-06 1.361263e-05 
##        13540        13553        13565        13586        13602        13621 
## 1.876553e-04 1.851816e-04 1.384216e-02 7.865246e-06 8.309411e-02 1.361263e-05 
##        13635        13636        13647        13656        13660        13674 
## 1.632376e-06 1.292210e-02 7.473835e-01 1.361263e-05 3.671491e-05 7.473835e-01 
##        13675        13682        13690        13732        13737        13742 
## 7.473835e-01 1.283902e-03 1.361263e-05 7.473835e-01 3.342656e-05 8.309411e-02 
##        13753        13755        13761        13777        13778        13782 
## 7.473835e-01 1.851816e-04 1.851816e-04 2.051463e-04 1.384216e-02 8.309411e-02 
##        13784        13791        13807        13892        13916        13962 
## 1.851816e-04 1.283902e-03 7.473835e-01 7.473835e-01 1.077222e-03 7.473835e-01 
##        13967        13989        14009        14035        14037        14060 
## 1.851816e-04 1.851816e-04 1.113006e-05 7.473835e-01 1.851816e-04 1.851816e-04 
##        14061        14064        14085        14095        14104        14110 
## 1.252681e-01 9.087979e-03 7.473835e-01 8.309411e-02 5.317688e-05 7.865246e-06 
##        14118        14119        14122        14125        14135        14137 
## 1.361263e-05 2.177740e-04 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 
##        14158        14187        14203        14204        14210        14216 
## 7.865246e-06 1.851816e-04 8.309411e-02 1.440165e-05 7.473835e-01 3.342656e-05 
##        14221        14256        14305        14311        14318        14321 
## 7.865246e-06 8.568722e-03 7.473835e-01 9.095206e-03 7.473835e-01 1.851816e-04 
##        14346        14358        14362        14368        14374        14403 
## 2.402165e-01 8.309411e-02 1.851816e-04 1.851816e-04 1.283902e-03 1.851816e-04 
##        14404        14414        14422        14435        14443        14481 
## 9.479464e-01 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.283902e-03 
##        14543        14571        14581        14592        14609        14628 
## 7.473835e-01 8.048715e-03 1.252681e-01 7.473835e-01 8.406202e-07 7.473835e-01 
##        14633        14635        14664        14683        14692        14725 
## 3.671491e-05 8.309411e-02 7.473835e-01 5.317688e-05 8.309411e-02 1.851816e-04 
##        14741        14743        14747        14751        14762        14780 
## 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 8.693217e-01 1.851816e-04 
##        14781        14787        14817        14819        14860        14895 
## 4.817649e-04 7.473835e-01 1.283902e-03 1.851816e-04 5.317688e-05 7.865246e-06 
##        14907        14925        14945        14947        14955        14963 
## 7.473835e-01 1.851816e-04 7.473835e-01 3.124682e-02 1.361263e-05 2.139593e-05 
##        15005        15024        15037        15096        15134        15143 
## 2.674842e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.865246e-06 1.415560e-01 
##        15194        15196        15200        15217        15220        15242 
## 8.309411e-02 3.671491e-05 7.865246e-06 6.987382e-05 1.361263e-05 3.342656e-05 
##        15249 
## 7.473835e-01
hist(eigenvector_cetrality, labels = TRUE, ylim = c(0,1000), xlab = "Eigenvector Centrality", main = "Histograma de los Valores de Eigenvector Centrality")

Según este histograma, hay nodos que tienen un eigenvector centrality mayor a 0.8. Veamos Cuáles son:

which(eigenvector_cetrality >=0.8)
##   134   679  1175  1467  1833  2316  2329  2426  2427  2660  2846  3009  3200 
##    15    56    90   110   130   157   158   169   170   194   206   217   236 
##  3265  3516  4010  4730  5049  5714  5846  5920  5996  6630  6815  6869  8123 
##   239   259   289   331   360   404   409   423   430   472   482   486   576 
##  8992  9098  9659 10974 11234 11707 11735 12147 12216 12335 12707 13000 14404 
##   630   638   672   761   778   806   809   835   839   843   879   903   997 
## 14762 
##  1019
colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
scaled_eigen = (eigenvector_cetrality * 100) + 1
colors <- colorfunc(max(scaled_eigen))
V(users_projected)$color <- colors[scaled_eigen]
V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = format(round(eigenvector_cetrality, 2), nsmall = 1),
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Noticias: Nodos según el Eigenvector Centrality")

plot(users_projected, 
     vertex.label = NA,
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Usuarios: Nodos según el Eigenvector Centrality")

Page Rank Centrality

page_rank = page.rank(users_projected)$vector
page_rank
##           10           11           41           51          114           67 
## 0.0011713097 0.0009388818 0.0003482703 0.0009341838 0.0002651061 0.0010698138 
##           78           82           85           98          107          128 
## 0.0007080711 0.0011368758 0.0002029969 0.0010698138 0.0011713097 0.0008358283 
##          132          133          134          143          144          169 
## 0.0004481219 0.0003217516 0.0013881179 0.0004175369 0.0003482703 0.0011713097 
##          182          187          189          203          231          234 
## 0.0004594431 0.0006438881 0.0010698138 0.0009341838 0.0009341838 0.0011713097 
##          246          254          257          258          281          306 
## 0.0007080711 0.0012193089 0.0009388818 0.0015886603 0.0010698138 0.0006438881 
##          345          349          354          376          393          398 
## 0.0009388818 0.0009388818 0.0010698138 0.0004873581 0.0005565868 0.0009388818 
##          448          456          466          470          471          478 
## 0.0010698138 0.0004481219 0.0016721165 0.0010698138 0.0004996982 0.0009341838 
##          499          519          521          522          529          533 
## 0.0009388818 0.0003227964 0.0009341838 0.0016737323 0.0009341838 0.0009388818 
##          568          595          620          639          648          656 
## 0.0015476963 0.0003742665 0.0010698138 0.0009388818 0.0004873581 0.0011713097 
##          657          679          697          743          771          796 
## 0.0006163682 0.0013881179 0.0007080711 0.0004175369 0.0016737323 0.0009388818 
##          822          837          838          840          841          859 
## 0.0009388818 0.0004175369 0.0006387061 0.0010698138 0.0004481219 0.0009341838 
##          861          873          917          940          946          948 
## 0.0009388818 0.0009388818 0.0010698138 0.0016141220 0.0009388818 0.0004996982 
##          968          973          976          994         1000         1002 
## 0.0008208890 0.0011713097 0.0006438881 0.0010698138 0.0010698138 0.0004594431 
##         1024         1031         1032         1039         1055         1076 
## 0.0011713097 0.0006387061 0.0008358283 0.0011713097 0.0004175369 0.0010698138 
##         1102         1110         1138         1163         1172         1175 
## 0.0011713097 0.0012785422 0.0011713097 0.0016762313 0.0011713097 0.0013881179 
##         1209         1214         1218         1223         1224         1257 
## 0.0009341838 0.0011713097 0.0010698138 0.0011713097 0.0010698138 0.0011713097 
##         1258         1280         1307         1313         1329         1362 
## 0.0006438881 0.0011713097 0.0007378925 0.0004594431 0.0011713097 0.0002651061 
##         1412         1415         1416         1424         1429         1445 
## 0.0010698138 0.0009341838 0.0010698138 0.0009341838 0.0003482703 0.0004873581 
##         1462         1467         1481         1483         1494         1507 
## 0.0003482703 0.0013881179 0.0009341838 0.0006387061 0.0004594431 0.0010698138 
##         1544         1559         1596         1598         1639         1657 
## 0.0016737323 0.0014386494 0.0010698138 0.0003482703 0.0007080711 0.0003217516 
##         1660         1705         1709         1718         1739         1752 
## 0.0010698138 0.0011713097 0.0009341838 0.0010848986 0.0007080711 0.0009341838 
##         1760         1790         1826         1833         1849         1884 
## 0.0007080711 0.0009388818 0.0002923049 0.0018620013 0.0010698138 0.0007080711 
##         1898         1902         1924         1933         1984         1994 
## 0.0016737323 0.0009341838 0.0009388818 0.0011713097 0.0011713097 0.0011713097 
##         2001         2011         2019         2026         2042         2063 
## 0.0009388818 0.0007080711 0.0006438881 0.0010698138 0.0021907777 0.0008358283 
##         2084         2129         2143         2149         2188         2192 
## 0.0010698138 0.0010698138 0.0010698138 0.0010698138 0.0011478567 0.0009388818 
##         2193         2199         2227         2250         2286         2293 
## 0.0010698138 0.0006387061 0.0015476963 0.0008358283 0.0011713097 0.0009341838 
##         2316         2329         2330         2335         2349         2350 
## 0.0013881179 0.0013881179 0.0009388818 0.0007080711 0.0004594431 0.0010698138 
##         2377         2380         2388         2393         2405         2415 
## 0.0004873581 0.0010698138 0.0011713097 0.0007080711 0.0004175369 0.0009341838 
##         2426         2427         2460         2462         2466         2471 
## 0.0021799494 0.0030622740 0.0006387061 0.0010698138 0.0004996982 0.0010698138 
##         2484         2491         2492         2502         2504         2516 
## 0.0011713097 0.0004594431 0.0011713097 0.0011713097 0.0009341838 0.0006438881 
##         2524         2526         2527         2533         2542         2549 
## 0.0007080711 0.0010593073 0.0010698138 0.0002894517 0.0010698138 0.0011713097 
##         2557         2562         2582         2596         2601         2603 
## 0.0008358283 0.0011478567 0.0004481219 0.0015348569 0.0011713097 0.0009341838 
##         2623         2660         2663         2701         2720         2730 
## 0.0005565868 0.0013881179 0.0012131444 0.0005565868 0.0006438881 0.0009388818 
##         2738         2795         2806         2811         2820         2835 
## 0.0009388818 0.0010698138 0.0002207343 0.0010698138 0.0002696208 0.0010698138 
##         2844         2846         2849         2861         2872         2876 
## 0.0010698138 0.0013881179 0.0010698138 0.0003217516 0.0002900729 0.0009341838 
##         2908         2920         2951         2961         2986         2987 
## 0.0011713097 0.0011713097 0.0004873581 0.0007080711 0.0009341838 0.0005565868 
##         3009         3020         3029         3051         3058         3065 
## 0.0013881179 0.0004594431 0.0010698138 0.0011713097 0.0009388818 0.0010698138 
##         3066         3091         3103         3119         3134         3136 
## 0.0011713097 0.0010698138 0.0005565868 0.0010698138 0.0004175369 0.0006438881 
##         3137         3150         3152         3158         3167         3186 
## 0.0004996982 0.0010698138 0.0017612924 0.0012513715 0.0005565868 0.0010698138 
##         3187         3200         3230         3260         3265         3278 
## 0.0014898330 0.0017529683 0.0011713097 0.0002580986 0.0015990236 0.0009388818 
##         3298         3314         3327         3345         3350         3356 
## 0.0010698138 0.0010698138 0.0010698138 0.0010698138 0.0011713097 0.0005118496 
##         3384         3397         3401         3404         3408         3411 
## 0.0010698138 0.0012075695 0.0006438881 0.0007080711 0.0010698138 0.0007080711 
##         3443         3459         3461         3469         3491         3505 
## 0.0010698138 0.0010698138 0.0003742665 0.0009341838 0.0006387061 0.0009388818 
##         3516         3519         3533         3549         3554         3557 
## 0.0022102613 0.0015476963 0.0011713097 0.0006438881 0.0009341838 0.0010698138 
##         3571         3577         3595         3596         3635         3648 
## 0.0011713097 0.0007080711 0.0007080711 0.0009341838 0.0004594431 0.0010698138 
##         3651         3723         3727         3728         3733         3750 
## 0.0009341838 0.0011713097 0.0011233504 0.0009341838 0.0005118496 0.0011713097 
##         3752         3753         3790         3833         3845         3857 
## 0.0009341838 0.0004594431 0.0011713097 0.0010698138 0.0003227964 0.0009388818 
##         3873         3893         3940         3965         3987         3989 
## 0.0011309105 0.0011713097 0.0007080711 0.0004873581 0.0006387061 0.0009388818 
##         4010         4011         4014         4068         4070         4080 
## 0.0013881179 0.0005565868 0.0010698138 0.0008208890 0.0010698138 0.0003742665 
##         4081         4102         4124         4159         4214         4229 
## 0.0010698138 0.0011713097 0.0008358283 0.0011713097 0.0004873581 0.0010698138 
##         4243         4245         4273         4276         4303         4304 
## 0.0010698138 0.0004873581 0.0010698138 0.0009388818 0.0011713097 0.0009341838 
##         4310         4323         4350         4352         4369         4374 
## 0.0011713097 0.0010698138 0.0002580986 0.0002894517 0.0010698138 0.0005118496 
##         4384         4432         4461         4470         4472         4476 
## 0.0017390477 0.0010698138 0.0008358283 0.0009388818 0.0011713097 0.0011713097 
##         4489         4526         4536         4542         4550         4590 
## 0.0015886603 0.0010698138 0.0011713097 0.0009388818 0.0004481219 0.0004435801 
##         4600         4615         4633         4667         4705         4708 
## 0.0011713097 0.0004873581 0.0010698138 0.0010698138 0.0005565868 0.0011713097 
##         4730         4750         4751         4756         4760         4792 
## 0.0013881179 0.0011713097 0.0005118496 0.0005118496 0.0010698138 0.0009341838 
##         4800         4801         4820         4822         4823         4833 
## 0.0002723135 0.0006438881 0.0009341838 0.0011713097 0.0004481219 0.0011713097 
##         4843         4846         4862         4864         4875         4879 
## 0.0012785422 0.0011713097 0.0005565868 0.0010698138 0.0005118496 0.0008358283 
##         4890         4904         4910         4921         4930         4954 
## 0.0009388818 0.0006387061 0.0010698138 0.0009341838 0.0006272817 0.0006387061 
##         4964         4982         5014         5015         5044         5049 
## 0.0005118496 0.0006387061 0.0003482703 0.0011713097 0.0005565868 0.0013881179 
##         5055         5057         5072         5103         5115         5120 
## 0.0010593073 0.0010698138 0.0010698138 0.0008358283 0.0016737323 0.0017314597 
##         5132         5136         5146         5179         5189         5223 
## 0.0003742665 0.0008791931 0.0007080711 0.0011713097 0.0007080711 0.0010698138 
##         5231         5251         5292         5293         5327         5331 
## 0.0011713097 0.0004873581 0.0004873581 0.0011713097 0.0011713097 0.0009388818 
##         5342         5359         5423         5424         5438         5446 
## 0.0010698138 0.0006387061 0.0010698138 0.0006387061 0.0010698138 0.0007080711 
##         5453         5461         5466         5507         5508         5531 
## 0.0009341838 0.0002723135 0.0020169136 0.0010593073 0.0010354461 0.0010698138 
##         5547         5552         5554         5556         5564         5579 
## 0.0011713097 0.0016721165 0.0009388818 0.0010698138 0.0006438881 0.0002599620 
##         5583         5597         5624         5666         5670         5688 
## 0.0010698138 0.0005118496 0.0011713097 0.0011713097 0.0011713097 0.0011713097 
##         5707         5714         5726         5731         5771         5793 
## 0.0011713097 0.0013881179 0.0010698138 0.0009388818 0.0010698138 0.0011713097 
##         5846         5849         5867         5881         5886         5899 
## 0.0013881179 0.0010698138 0.0011713097 0.0011713097 0.0004996982 0.0007080711 
##         5901         5902         5904         5905         5906         5911 
## 0.0011713097 0.0011713097 0.0011713097 0.0004996982 0.0010698138 0.0009341838 
##         5912         5918         5920         5939         5948         5962 
## 0.0009388818 0.0011713097 0.0013881179 0.0005565868 0.0007080711 0.0015886603 
##         5965         5973         5994         5996         5999         6003 
## 0.0010698138 0.0010698138 0.0011713097 0.0030869325 0.0005565868 0.0011713097 
##         6009         6018         6022         6054         6078         6085 
## 0.0012785422 0.0017390477 0.0006387061 0.0023188414 0.0010105412 0.0011713097 
##         6118         6121         6125         6134         6145         6163 
## 0.0010698138 0.0010698138 0.0009341838 0.0006438881 0.0005118496 0.0010698138 
##         6169         6173         6190         6202         6221         6223 
## 0.0006438881 0.0003227964 0.0011713097 0.0003742665 0.0009388818 0.0010698138 
##         6258         6322         6336         6345         6349         6350 
## 0.0010698138 0.0009388818 0.0007080711 0.0003500186 0.0006387061 0.0006438881 
##         6354         6367         6370         6373         6391         6404 
## 0.0009388818 0.0011713097 0.0011713097 0.0004996982 0.0011713097 0.0009388818 
##         6451         6472         6498         6505         6554         6563 
## 0.0010698138 0.0011713097 0.0011713097 0.0010698138 0.0010698138 0.0009388818 
##         6576         6591         6600         6630         6647         6679 
## 0.0009341838 0.0015886603 0.0004873581 0.0018620013 0.0003500186 0.0011713097 
##         6690         6695         6742         6757         6764         6784 
## 0.0006438881 0.0011713097 0.0010698138 0.0010698138 0.0009388818 0.0015886603 
##         6785         6815         6821         6857         6860         6869 
## 0.0011713097 0.0023655262 0.0010698138 0.0006387061 0.0010698138 0.0013881179 
##         6876         6880         6901         6914         6918         6920 
## 0.0003500186 0.0016762313 0.0009388818 0.0002153317 0.0002508441 0.0010698138 
##         6938         6939         6943         6946         6949         6955 
## 0.0011713097 0.0002651061 0.0011713097 0.0011713097 0.0010698138 0.0009341838 
##         6962         7026         7041         7048         7082         7103 
## 0.0015886603 0.0010698138 0.0009388818 0.0010698138 0.0010698138 0.0010698138 
##         7109         7116         7129         7137         7194         7202 
## 0.0006438881 0.0005565868 0.0010698138 0.0007080711 0.0011713097 0.0010698138 
##         7242         7261         7277         7295         7313         7316 
## 0.0010698138 0.0011713097 0.0003500186 0.0004996982 0.0009388818 0.0011713097 
##         7335         7337         7345         7352         7367         7373 
## 0.0011713097 0.0004175369 0.0005565868 0.0011713097 0.0010698138 0.0016737323 
##         7375         7392         7397         7398         7401         7430 
## 0.0010698138 0.0010698138 0.0005565868 0.0011713097 0.0009388818 0.0004873581 
##         7456         7458         7461         7472         7480         7482 
## 0.0009388818 0.0006387061 0.0009341838 0.0008358283 0.0010698138 0.0011713097 
##         7483         7508         7514         7564         7566         7569 
## 0.0019230111 0.0011713097 0.0010698138 0.0003482703 0.0009341838 0.0012030072 
##         7578         7619         7623         7624         7649         7697 
## 0.0011713097 0.0010698138 0.0010698138 0.0017390477 0.0007080711 0.0009388818 
##         7718         7731         7746         7756         7762         7765 
## 0.0011713097 0.0011713097 0.0006387061 0.0016737323 0.0002923049 0.0009341838 
##         7772         7779         7825         7830         7837         7850 
## 0.0014647940 0.0010698138 0.0005118496 0.0005565868 0.0009341838 0.0007080711 
##         7859         7862         7887         7890         7902         7904 
## 0.0006387061 0.0005118496 0.0011713097 0.0007080711 0.0004594431 0.0010698138 
##         7905         7941         7962         7964         7966         7983 
## 0.0011713097 0.0011713097 0.0004873581 0.0009388818 0.0009341838 0.0011713097 
##         8006         8015         8030         8077         8113         8123 
## 0.0009388818 0.0011713097 0.0005118496 0.0011713097 0.0011713097 0.0013881179 
##         8133         8134         8168         8174         8181         8183 
## 0.0009341838 0.0017814425 0.0006387061 0.0004594431 0.0006438881 0.0011713097 
##         8208         8220         8223         8253         8267         8293 
## 0.0011713097 0.0010698138 0.0010698138 0.0006387061 0.0012047979 0.0011713097 
##         8294         8309         8338         8342         8362         8365 
## 0.0010698138 0.0012560040 0.0009341838 0.0011713097 0.0005565868 0.0006438881 
##         8370         8373         8382         8393         8413         8426 
## 0.0010105412 0.0009341838 0.0011713097 0.0004996982 0.0009388818 0.0009341838 
##         8485         8542         8546         8566         8593         8609 
## 0.0010698138 0.0011713097 0.0010698138 0.0009341838 0.0010698138 0.0016737323 
##         8627         8663         8679         8708         8742         8746 
## 0.0003742665 0.0004873581 0.0006438881 0.0005118496 0.0009388818 0.0004594431 
##         8751         8761         8783         8787         8798         8825 
## 0.0016721165 0.0011713097 0.0004996982 0.0004996982 0.0011713097 0.0009341838 
##         8831         8850         8868         8878         8880         8894 
## 0.0011713097 0.0009388818 0.0010698138 0.0011233504 0.0012485819 0.0009341838 
##         8914         8931         8939         8953         8957         8992 
## 0.0006387061 0.0011713097 0.0006387061 0.0009388818 0.0004996982 0.0013881179 
##         8997         9015         9018         9025         9048         9061 
## 0.0009341838 0.0010698138 0.0002696208 0.0010698138 0.0004594431 0.0004996982 
##         9095         9098         9117         9129         9140         9163 
## 0.0011713097 0.0018620013 0.0011713097 0.0026597561 0.0011295432 0.0005565868 
##         9204         9210         9228         9229         9250         9253 
## 0.0010698138 0.0010698138 0.0011713097 0.0011713097 0.0012485819 0.0009341838 
##         9309         9310         9320         9341         9350         9355 
## 0.0004873581 0.0010698138 0.0003227964 0.0010698138 0.0009341838 0.0010698138 
##         9358         9373         9384         9407         9413         9424 
## 0.0007980112 0.0009388818 0.0004873581 0.0007080711 0.0006387061 0.0011713097 
##         9481         9486         9500         9553         9568         9570 
## 0.0004996982 0.0009388818 0.0009388818 0.0004594431 0.0011713097 0.0007080711 
##         9596         9607         9619         9641         9652         9659 
## 0.0006438881 0.0002894517 0.0011713097 0.0007080711 0.0004594431 0.0015990236 
##         9661         9664         9679         9682         9684         9714 
## 0.0010698138 0.0005565868 0.0010105412 0.0010698138 0.0011713097 0.0008358283 
##         9726         9763         9766         9782         9785         9792 
## 0.0022391695 0.0022391695 0.0006438881 0.0002820643 0.0010698138 0.0007080711 
##         9794         9809         9816         9834         9848         9851 
## 0.0010698138 0.0006438881 0.0011713097 0.0011713097 0.0017814425 0.0005565868 
##         9857         9877         9895         9905         9920        10003 
## 0.0001589419 0.0010698138 0.0002820643 0.0011713097 0.0006438881 0.0011713097 
##        10012        10054        10105        10110        10117        10118 
## 0.0011713097 0.0015003231 0.0014189756 0.0005118496 0.0009388818 0.0002820643 
##        10130        10155        10178        10201        10206        10209 
## 0.0010698138 0.0010698138 0.0012785422 0.0010698138 0.0019175970 0.0010698138 
##        10212        10241        10262        10270        10279        10290 
## 0.0004481219 0.0026597561 0.0006438881 0.0010698138 0.0006387061 0.0011713097 
##        10303        10364        10371        10386        10404        10423 
## 0.0011713097 0.0015886603 0.0010698138 0.0019670350 0.0012173047 0.0007080711 
##        10439        10449        10475        10480        10487        10500 
## 0.0011713097 0.0009341838 0.0001752357 0.0007080711 0.0011713097 0.0010698138 
##        10512        10516        10527        10544        10549        10568 
## 0.0004996982 0.0004873581 0.0010698138 0.0009341838 0.0011713097 0.0009341838 
##        10572        10582        10590        10638        10650        10694 
## 0.0011713097 0.0007080711 0.0009341838 0.0018500530 0.0012809606 0.0004873581 
##        10708        10724        10730        10736        10759        10771 
## 0.0004175369 0.0006387061 0.0010698138 0.0011713097 0.0010698138 0.0004996982 
##        10774        10776        10782        10802        10808        10836 
## 0.0010698138 0.0005565868 0.0009388818 0.0010698138 0.0011713097 0.0003217516 
##        10862        10874        10882        10886        10891        10906 
## 0.0010698138 0.0004594431 0.0009341838 0.0008358283 0.0011233504 0.0010698138 
##        10920        10929        10944        10952        10974        10995 
## 0.0009341838 0.0010698138 0.0010698138 0.0006438881 0.0013881179 0.0011713097 
##        11011        11025        11044        11073        11074        11123 
## 0.0006438881 0.0011713097 0.0004996982 0.0002723135 0.0009341838 0.0005565868 
##        11132        11142        11146        11156        11164        11171 
## 0.0009388818 0.0005565868 0.0010698138 0.0003482703 0.0002900729 0.0003482703 
##        11178        11217        11225        11234        11257        11296 
## 0.0007080711 0.0011713097 0.0010698138 0.0029310713 0.0010698138 0.0011713097 
##        11302        11305        11342        11352        11388        11390 
## 0.0004175369 0.0007080711 0.0016260007 0.0006387061 0.0005118496 0.0010698138 
##        11396        11417        11443        11456        11457        11461 
## 0.0008358283 0.0011713097 0.0004873581 0.0003500186 0.0004481219 0.0002508441 
##        11504        11527        11559        11560        11592        11606 
## 0.0006438881 0.0009388818 0.0009341838 0.0011713097 0.0004594431 0.0010698138 
##        11608        11642        11664        11671        11678        11700 
## 0.0010901086 0.0010698138 0.0009388818 0.0011713097 0.0007080711 0.0010698138 
##        11704        11707        11728        11729        11735        11753 
## 0.0010698138 0.0018620013 0.0010593073 0.0003227964 0.0013881179 0.0005565868 
##        11757        11818        11820        11839        11843        11859 
## 0.0010698138 0.0009388818 0.0007080711 0.0009388818 0.0005118496 0.0009341838 
##        11862        11887        11896        11935        11980        11988 
## 0.0009388818 0.0017672715 0.0011713097 0.0010698138 0.0004175369 0.0010698138 
##        12016        12030        12032        12049        12051        12075 
## 0.0009341838 0.0010698138 0.0011713097 0.0009341838 0.0005118496 0.0011713097 
##        12084        12091        12109        12114        12117        12128 
## 0.0011713097 0.0010698138 0.0023392465 0.0009388818 0.0006387061 0.0008358283 
##        12147        12160        12166        12190        12216        12236 
## 0.0013881179 0.0009388818 0.0003217516 0.0011713097 0.0013881179 0.0009341838 
##        12283        12307        12335        12367        12372        12376 
## 0.0004594431 0.0005118496 0.0013881179 0.0011713097 0.0008358283 0.0011713097 
##        12380        12382        12389        12395        12397        12408 
## 0.0009341838 0.0006387061 0.0004594431 0.0004594431 0.0009341838 0.0010698138 
##        12427        12439        12450        12452        12465        12468 
## 0.0011713097 0.0003500186 0.0009388818 0.0009388818 0.0010698138 0.0007080711 
##        12490        12496        12522        12527        12528        12537 
## 0.0009341838 0.0009341838 0.0006438881 0.0005565868 0.0010698138 0.0010698138 
##        12546        12550        12552        12554        12561        12568 
## 0.0006438881 0.0011713097 0.0011713097 0.0004175369 0.0012173047 0.0011713097 
##        12570        12579        12593        12607        12609        12622 
## 0.0010698138 0.0010698138 0.0004873581 0.0010698138 0.0011713097 0.0006387061 
##        12648        12705        12707        12739        12751        12761 
## 0.0011713097 0.0009388818 0.0013881179 0.0003227964 0.0009388818 0.0004608206 
##        12782        12799        12804        12806        12816        12843 
## 0.0009388818 0.0010698138 0.0006438881 0.0010698138 0.0003742665 0.0006387061 
##        12887        12888        12894        12901        12906        12918 
## 0.0010698138 0.0010698138 0.0011713097 0.0016762313 0.0010698138 0.0006387061 
##        12933        12943        12948        12956        12964        12968 
## 0.0008741995 0.0005565868 0.0022391695 0.0012785422 0.0009388818 0.0010698138 
##        12980        12984        13000        13035        13052        13087 
## 0.0011713097 0.0010698138 0.0013881179 0.0010698138 0.0009388818 0.0016737323 
##        13092        13104        13111        13133        13136        13137 
## 0.0011713097 0.0011713097 0.0009341838 0.0011713097 0.0014647940 0.0009388818 
##        13138        13143        13150        13154        13159        13188 
## 0.0004175369 0.0010698138 0.0004996982 0.0007080711 0.0011713097 0.0010698138 
##        13252        13261        13263        13284        13335        13336 
## 0.0010698138 0.0011713097 0.0002723135 0.0007080711 0.0007080711 0.0010698138 
##        13341        13360        13396        13450        13469        13497 
## 0.0011713097 0.0009341838 0.0010698138 0.0010698138 0.0003742665 0.0007080711 
##        13540        13553        13565        13586        13602        13621 
## 0.0014189756 0.0011713097 0.0004175369 0.0006438881 0.0009341838 0.0007080711 
##        13635        13636        13647        13656        13660        13674 
## 0.0004481219 0.0004996982 0.0010698138 0.0007080711 0.0006387061 0.0010698138 
##        13675        13682        13690        13732        13737        13742 
## 0.0010698138 0.0009388818 0.0007080711 0.0010698138 0.0005118496 0.0009341838 
##        13753        13755        13761        13777        13778        13782 
## 0.0010698138 0.0011713097 0.0011713097 0.0023200404 0.0004175369 0.0009341838 
##        13784        13791        13807        13892        13916        13962 
## 0.0011713097 0.0009388818 0.0010698138 0.0010698138 0.0002153317 0.0010698138 
##        13967        13989        14009        14035        14037        14060 
## 0.0011713097 0.0011713097 0.0005565868 0.0010698138 0.0011713097 0.0011713097 
##        14061        14064        14085        14095        14104        14110 
## 0.0004594431 0.0003500186 0.0010698138 0.0009341838 0.0008358283 0.0006438881 
##        14118        14119        14122        14125        14135        14137 
## 0.0007080711 0.0015476963 0.0010698138 0.0010698138 0.0010698138 0.0011713097 
##        14158        14187        14203        14204        14210        14216 
## 0.0006438881 0.0011713097 0.0009341838 0.0007807693 0.0010698138 0.0005118496 
##        14221        14256        14305        14311        14318        14321 
## 0.0006438881 0.0003217516 0.0010698138 0.0005384504 0.0010698138 0.0011713097 
##        14346        14358        14362        14368        14374        14403 
## 0.0021005459 0.0009341838 0.0011713097 0.0011713097 0.0009388818 0.0011713097 
##        14404        14414        14422        14435        14443        14481 
## 0.0041089722 0.0011713097 0.0010698138 0.0010698138 0.0006387061 0.0009388818 
##        14543        14571        14581        14592        14609        14628 
## 0.0010698138 0.0002820643 0.0004594431 0.0010698138 0.0002599620 0.0010698138 
##        14633        14635        14664        14683        14692        14725 
## 0.0006387061 0.0009341838 0.0010698138 0.0008358283 0.0009341838 0.0011713097 
##        14741        14743        14747        14751        14762        14780 
## 0.0011713097 0.0010698138 0.0011713097 0.0010698138 0.0013881179 0.0011713097 
##        14781        14787        14817        14819        14860        14895 
## 0.0004691925 0.0010698138 0.0009388818 0.0011713097 0.0008358283 0.0006438881 
##        14907        14925        14945        14947        14955        14963 
## 0.0010698138 0.0011713097 0.0010698138 0.0004873581 0.0007080711 0.0012106318 
##        15005        15024        15037        15096        15134        15143 
## 0.0018075839 0.0011713097 0.0011713097 0.0010698138 0.0006438881 0.0014647940 
##        15194        15196        15200        15217        15220        15242 
## 0.0009341838 0.0006387061 0.0006438881 0.0010105412 0.0007080711 0.0005118496 
##        15249 
## 0.0010698138
hist(page_rank, labels = TRUE, ylim = c(0,500), xlim = c(0,0.005), xlab = "PageRank Centrality", main = "Histograma de los Valores de PageRank Centrality")

colorfunc <- colorRampPalette(c( "Medium Slate Blue",
                                 "Magenta",
                                 "Maroon 2",
                                 "Purple",
                                 "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue",
                                 "Light Steel Blue 1",
                                 "Royal Blue 2"))
scaled_page_rank = (page_rank * 1000) + 1
colors <- colorfunc(max(scaled_page_rank))
V(users_projected)$color <- colors[scaled_page_rank]
V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = format(round(scaled_page_rank), nsmall = 1),
     vertex.size = 2,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Usuarios: Nodos según Page Rank Score Escalado")

plot(users_projected, 
     vertex.label = NA,
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout=layout_components,
     main = "Proyección Red Usuarios: Nodos según Page Rank Score Escalado")

Authorities & Hubs

Authorities

authority = authority.score(users_projected)$vector
authority
##           10           11           41           51          114           67 
## 1.851816e-04 1.283902e-03 3.094893e-02 8.309411e-02 8.051461e-03 7.473835e-01 
##           78           82           85           98          107          128 
## 1.361263e-05 1.320908e-03 3.240013e-04 7.473835e-01 1.851816e-04 5.317688e-05 
##          132          133          134          143          144          169 
## 1.632376e-06 8.568722e-03 8.693217e-01 1.384216e-02 3.094893e-02 1.851816e-04 
##          182          187          189          203          231          234 
## 1.252681e-01 7.865246e-06 7.473835e-01 8.309411e-02 8.309411e-02 1.851816e-04 
##          246          254          257          258          281          306 
## 1.361263e-05 1.506834e-02 1.283902e-03 1.955626e-04 7.473835e-01 7.865246e-06 
##          345          349          354          376          393          398 
## 1.283902e-03 1.283902e-03 7.473835e-01 3.124682e-02 1.113006e-05 1.283902e-03 
##          448          456          466          470          471          478 
## 7.473835e-01 1.632376e-06 2.210498e-04 7.473835e-01 1.292210e-02 8.309411e-02 
##          499          519          521          522          529          533 
## 1.283902e-03 2.829945e-02 8.309411e-02 1.716172e-01 8.309411e-02 1.283902e-03 
##          568          595          620          639          648          656 
## 2.177740e-04 3.192423e-06 7.473835e-01 1.283902e-03 3.124682e-02 1.851816e-04 
##          657          679          697          743          771          796 
## 3.914832e-02 8.693217e-01 1.361263e-05 1.384216e-02 1.716172e-01 1.283902e-03 
##          822          837          838          840          841          859 
## 1.283902e-03 1.384216e-02 3.671491e-05 7.473835e-01 1.632376e-06 8.309411e-02 
##          861          873          917          940          946          948 
## 1.283902e-03 1.283902e-03 7.473835e-01 2.196020e-01 1.283902e-03 1.292210e-02 
##          968          973          976          994         1000         1002 
## 1.376629e-01 1.851816e-04 7.865246e-06 7.473835e-01 7.473835e-01 1.252681e-01 
##         1024         1031         1032         1039         1055         1076 
## 1.851816e-04 3.671491e-05 5.317688e-05 1.851816e-04 1.384216e-02 7.473835e-01 
##         1102         1110         1138         1163         1172         1175 
## 1.851816e-04 9.947152e-02 1.851816e-04 1.923103e-04 1.851816e-04 8.693217e-01 
##         1209         1214         1218         1223         1224         1257 
## 8.309411e-02 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 1.851816e-04 
##         1258         1280         1307         1313         1329         1362 
## 7.865246e-06 1.851816e-04 1.147608e-05 1.252681e-01 1.851816e-04 8.051461e-03 
##         1412         1415         1416         1424         1429         1445 
## 7.473835e-01 8.309411e-02 7.473835e-01 8.309411e-02 3.094893e-02 3.124682e-02 
##         1462         1467         1481         1483         1494         1507 
## 3.094893e-02 8.693217e-01 8.309411e-02 3.671491e-05 1.252681e-01 7.473835e-01 
##         1544         1559         1596         1598         1639         1657 
## 1.716172e-01 1.016310e-01 7.473835e-01 3.094893e-02 1.361263e-05 8.568722e-03 
##         1660         1705         1709         1718         1739         1752 
## 7.473835e-01 1.851816e-04 8.309411e-02 5.977311e-06 1.361263e-05 8.309411e-02 
##         1760         1790         1826         1833         1849         1884 
## 1.361263e-05 1.283902e-03 4.206519e-05 8.273087e-01 7.473835e-01 1.361263e-05 
##         1898         1902         1924         1933         1984         1994 
## 1.716172e-01 8.309411e-02 1.283902e-03 1.851816e-04 1.851816e-04 1.851816e-04 
##         2001         2011         2019         2026         2042         2063 
## 1.283902e-03 1.361263e-05 7.865246e-06 7.473835e-01 6.573193e-03 5.317688e-05 
##         2084         2129         2143         2149         2188         2192 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 9.183034e-02 1.283902e-03 
##         2193         2199         2227         2250         2286         2293 
## 7.473835e-01 3.671491e-05 2.177740e-04 5.317688e-05 1.851816e-04 8.309411e-02 
##         2316         2329         2330         2335         2349         2350 
## 8.693217e-01 8.693217e-01 1.283902e-03 1.361263e-05 1.252681e-01 7.473835e-01 
##         2377         2380         2388         2393         2405         2415 
## 3.124682e-02 7.473835e-01 1.851816e-04 1.361263e-05 1.384216e-02 8.309411e-02 
##         2426         2427         2460         2462         2466         2471 
## 9.484796e-01 9.216813e-01 3.671491e-05 7.473835e-01 1.292210e-02 7.473835e-01 
##         2484         2491         2492         2502         2504         2516 
## 1.851816e-04 1.252681e-01 1.851816e-04 1.851816e-04 8.309411e-02 7.865246e-06 
##         2524         2526         2527         2533         2542         2549 
## 1.361263e-05 1.892283e-05 7.473835e-01 3.899759e-07 7.473835e-01 1.851816e-04 
##         2557         2562         2582         2596         2601         2603 
## 5.317688e-05 9.183034e-02 1.632376e-06 2.205150e-01 1.851816e-04 8.309411e-02 
##         2623         2660         2663         2701         2720         2730 
## 1.113006e-05 8.693217e-01 1.951956e-01 1.113006e-05 7.865246e-06 1.283902e-03 
##         2738         2795         2806         2811         2820         2835 
## 1.283902e-03 7.473835e-01 6.423139e-04 7.473835e-01 1.534919e-06 7.473835e-01 
##         2844         2846         2849         2861         2872         2876 
## 7.473835e-01 8.693217e-01 7.473835e-01 8.568722e-03 4.415451e-04 8.309411e-02 
##         2908         2920         2951         2961         2986         2987 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.361263e-05 8.309411e-02 1.113006e-05 
##         3009         3020         3029         3051         3058         3065 
## 8.693217e-01 1.252681e-01 7.473835e-01 1.851816e-04 1.283902e-03 7.473835e-01 
##         3066         3091         3103         3119         3134         3136 
## 1.851816e-04 7.473835e-01 1.113006e-05 7.473835e-01 1.384216e-02 7.865246e-06 
##         3137         3150         3152         3158         3167         3186 
## 1.292210e-02 7.473835e-01 8.318815e-05 2.075671e-01 1.113006e-05 7.473835e-01 
##         3187         3200         3230         3260         3265         3278 
## 1.441853e-01 8.788411e-01 1.851816e-04 3.859943e-03 8.967309e-01 1.283902e-03 
##         3298         3314         3327         3345         3350         3356 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 3.342656e-05 
##         3384         3397         3401         3404         3408         3411 
## 7.473835e-01 9.679743e-02 7.865246e-06 1.361263e-05 7.473835e-01 1.361263e-05 
##         3443         3459         3461         3469         3491         3505 
## 7.473835e-01 7.473835e-01 3.192423e-06 8.309411e-02 3.671491e-05 1.283902e-03 
##         3516         3519         3533         3549         3554         3557 
## 8.551731e-01 2.177740e-04 1.851816e-04 7.865246e-06 8.309411e-02 7.473835e-01 
##         3571         3577         3595         3596         3635         3648 
## 1.851816e-04 1.361263e-05 1.361263e-05 8.309411e-02 1.252681e-01 7.473835e-01 
##         3651         3723         3727         3728         3733         3750 
## 8.309411e-02 1.851816e-04 2.464828e-05 8.309411e-02 3.342656e-05 1.851816e-04 
##         3752         3753         3790         3833         3845         3857 
## 8.309411e-02 1.252681e-01 1.851816e-04 7.473835e-01 2.829945e-02 1.283902e-03 
##         3873         3893         3940         3965         3987         3989 
## 9.815029e-03 1.851816e-04 1.361263e-05 3.124682e-02 3.671491e-05 1.283902e-03 
##         4010         4011         4014         4068         4070         4080 
## 8.693217e-01 1.113006e-05 7.473835e-01 1.376629e-01 7.473835e-01 3.192423e-06 
##         4081         4102         4124         4159         4214         4229 
## 7.473835e-01 1.851816e-04 5.317688e-05 1.851816e-04 3.124682e-02 7.473835e-01 
##         4243         4245         4273         4276         4303         4304 
## 7.473835e-01 3.124682e-02 7.473835e-01 1.283902e-03 1.851816e-04 8.309411e-02 
##         4310         4323         4350         4352         4369         4374 
## 1.851816e-04 7.473835e-01 3.859943e-03 3.899759e-07 7.473835e-01 3.342656e-05 
##         4384         4432         4461         4470         4472         4476 
## 1.980357e-04 7.473835e-01 5.317688e-05 1.283902e-03 1.851816e-04 1.851816e-04 
##         4489         4526         4536         4542         4550         4590 
## 1.955626e-04 7.473835e-01 1.851816e-04 1.283902e-03 1.632376e-06 1.012641e-02 
##         4600         4615         4633         4667         4705         4708 
## 1.851816e-04 3.124682e-02 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 
##         4730         4750         4751         4756         4760         4792 
## 8.693217e-01 1.851816e-04 3.342656e-05 3.342656e-05 7.473835e-01 8.309411e-02 
##         4800         4801         4820         4822         4823         4833 
## 6.393403e-03 7.865246e-06 8.309411e-02 1.851816e-04 1.632376e-06 1.851816e-04 
##         4843         4846         4862         4864         4875         4879 
## 9.947152e-02 1.851816e-04 1.113006e-05 7.473835e-01 3.342656e-05 5.317688e-05 
##         4890         4904         4910         4921         4930         4954 
## 1.283902e-03 3.671491e-05 7.473835e-01 8.309411e-02 2.089353e-02 3.671491e-05 
##         4964         4982         5014         5015         5044         5049 
## 3.342656e-05 3.671491e-05 3.094893e-02 1.851816e-04 1.113006e-05 8.693217e-01 
##         5055         5057         5072         5103         5115         5120 
## 1.892283e-05 7.473835e-01 7.473835e-01 5.317688e-05 1.716172e-01 8.405604e-02 
##         5132         5136         5146         5179         5189         5223 
## 3.192423e-06 8.980721e-02 1.361263e-05 1.851816e-04 1.361263e-05 7.473835e-01 
##         5231         5251         5292         5293         5327         5331 
## 1.851816e-04 3.124682e-02 3.124682e-02 1.851816e-04 1.851816e-04 1.283902e-03 
##         5342         5359         5423         5424         5438         5446 
## 7.473835e-01 3.671491e-05 7.473835e-01 3.671491e-05 7.473835e-01 1.361263e-05 
##         5453         5461         5466         5507         5508         5531 
## 8.309411e-02 6.393403e-03 1.964649e-04 1.892283e-05 8.385015e-02 7.473835e-01 
##         5547         5552         5554         5556         5564         5579 
## 1.851816e-04 2.210498e-04 1.283902e-03 7.473835e-01 7.865246e-06 8.406202e-07 
##         5583         5597         5624         5666         5670         5688 
## 7.473835e-01 3.342656e-05 1.851816e-04 1.851816e-04 1.851816e-04 1.851816e-04 
##         5707         5714         5726         5731         5771         5793 
## 1.851816e-04 8.693217e-01 7.473835e-01 1.283902e-03 7.473835e-01 1.851816e-04 
##         5846         5849         5867         5881         5886         5899 
## 8.693217e-01 7.473835e-01 1.851816e-04 1.851816e-04 1.292210e-02 1.361263e-05 
##         5901         5902         5904         5905         5906         5911 
## 1.851816e-04 1.851816e-04 1.851816e-04 1.292210e-02 7.473835e-01 8.309411e-02 
##         5912         5918         5920         5939         5948         5962 
## 1.283902e-03 1.851816e-04 8.693217e-01 1.113006e-05 1.361263e-05 1.955626e-04 
##         5965         5973         5994         5996         5999         6003 
## 7.473835e-01 7.473835e-01 1.851816e-04 9.221897e-01 1.113006e-05 1.851816e-04 
##         6009         6018         6022         6054         6078         6085 
## 9.947152e-02 1.980357e-04 3.671491e-05 1.994648e-01 6.987382e-05 1.851816e-04 
##         6118         6121         6125         6134         6145         6163 
## 7.473835e-01 7.473835e-01 8.309411e-02 7.865246e-06 3.342656e-05 7.473835e-01 
##         6169         6173         6190         6202         6221         6223 
## 7.865246e-06 2.829945e-02 1.851816e-04 3.192423e-06 1.283902e-03 7.473835e-01 
##         6258         6322         6336         6345         6349         6350 
## 7.473835e-01 1.283902e-03 1.361263e-05 9.087979e-03 3.671491e-05 7.865246e-06 
##         6354         6367         6370         6373         6391         6404 
## 1.283902e-03 1.851816e-04 1.851816e-04 1.292210e-02 1.851816e-04 1.283902e-03 
##         6451         6472         6498         6505         6554         6563 
## 7.473835e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 
##         6576         6591         6600         6630         6647         6679 
## 8.309411e-02 1.955626e-04 3.124682e-02 8.273087e-01 9.087979e-03 1.851816e-04 
##         6690         6695         6742         6757         6764         6784 
## 7.865246e-06 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 1.955626e-04 
##         6785         6815         6821         6857         6860         6869 
## 1.851816e-04 9.728658e-01 7.473835e-01 3.671491e-05 7.473835e-01 8.693217e-01 
##         6876         6880         6901         6914         6918         6920 
## 9.087979e-03 1.923103e-04 1.283902e-03 1.077222e-03 7.570669e-08 7.473835e-01 
##         6938         6939         6943         6946         6949         6955 
## 1.851816e-04 8.051461e-03 1.851816e-04 1.851816e-04 7.473835e-01 8.309411e-02 
##         6962         7026         7041         7048         7082         7103 
## 1.955626e-04 7.473835e-01 1.283902e-03 7.473835e-01 7.473835e-01 7.473835e-01 
##         7109         7116         7129         7137         7194         7202 
## 7.865246e-06 1.113006e-05 7.473835e-01 1.361263e-05 1.851816e-04 7.473835e-01 
##         7242         7261         7277         7295         7313         7316 
## 7.473835e-01 1.851816e-04 9.087979e-03 1.292210e-02 1.283902e-03 1.851816e-04 
##         7335         7337         7345         7352         7367         7373 
## 1.851816e-04 1.384216e-02 1.113006e-05 1.851816e-04 7.473835e-01 1.716172e-01 
##         7375         7392         7397         7398         7401         7430 
## 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 1.283902e-03 3.124682e-02 
##         7456         7458         7461         7472         7480         7482 
## 1.283902e-03 3.671491e-05 8.309411e-02 5.317688e-05 7.473835e-01 1.851816e-04 
##         7483         7508         7514         7564         7566         7569 
## 1.947474e-04 1.851816e-04 7.473835e-01 3.094893e-02 8.309411e-02 1.292577e-02 
##         7578         7619         7623         7624         7649         7697 
## 1.851816e-04 7.473835e-01 7.473835e-01 1.980357e-04 1.361263e-05 1.283902e-03 
##         7718         7731         7746         7756         7762         7765 
## 1.851816e-04 1.851816e-04 3.671491e-05 1.716172e-01 4.206519e-05 8.309411e-02 
##         7772         7779         7825         7830         7837         7850 
## 1.415560e-01 7.473835e-01 3.342656e-05 1.113006e-05 8.309411e-02 1.361263e-05 
##         7859         7862         7887         7890         7902         7904 
## 3.671491e-05 3.342656e-05 1.851816e-04 1.361263e-05 1.252681e-01 7.473835e-01 
##         7905         7941         7962         7964         7966         7983 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.283902e-03 8.309411e-02 1.851816e-04 
##         8006         8015         8030         8077         8113         8123 
## 1.283902e-03 1.851816e-04 3.342656e-05 1.851816e-04 1.851816e-04 8.693217e-01 
##         8133         8134         8168         8174         8181         8183 
## 8.309411e-02 1.177450e-01 3.671491e-05 1.252681e-01 7.865246e-06 1.851816e-04 
##         8208         8220         8223         8253         8267         8293 
## 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.259357e-05 1.851816e-04 
##         8294         8309         8338         8342         8362         8365 
## 7.473835e-01 1.260691e-01 8.309411e-02 1.851816e-04 1.113006e-05 7.865246e-06 
##         8370         8373         8382         8393         8413         8426 
## 6.987382e-05 8.309411e-02 1.851816e-04 1.292210e-02 1.283902e-03 8.309411e-02 
##         8485         8542         8546         8566         8593         8609 
## 7.473835e-01 1.851816e-04 7.473835e-01 8.309411e-02 7.473835e-01 1.716172e-01 
##         8627         8663         8679         8708         8742         8746 
## 3.192423e-06 3.124682e-02 7.865246e-06 3.342656e-05 1.283902e-03 1.252681e-01 
##         8751         8761         8783         8787         8798         8825 
## 2.210498e-04 1.851816e-04 1.292210e-02 1.292210e-02 1.851816e-04 8.309411e-02 
##         8831         8850         8868         8878         8880         8894 
## 1.851816e-04 1.283902e-03 7.473835e-01 2.464828e-05 9.255031e-02 8.309411e-02 
##         8914         8931         8939         8953         8957         8992 
## 3.671491e-05 1.851816e-04 3.671491e-05 1.283902e-03 1.292210e-02 8.693217e-01 
##         8997         9015         9018         9025         9048         9061 
## 8.309411e-02 7.473835e-01 1.534919e-06 7.473835e-01 1.252681e-01 1.292210e-02 
##         9095         9098         9117         9129         9140         9163 
## 1.851816e-04 8.273087e-01 1.851816e-04 2.153154e-04 9.131307e-02 1.113006e-05 
##         9204         9210         9228         9229         9250         9253 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.851816e-04 9.255031e-02 8.309411e-02 
##         9309         9310         9320         9341         9350         9355 
## 3.124682e-02 7.473835e-01 2.829945e-02 7.473835e-01 8.309411e-02 7.473835e-01 
##         9358         9373         9384         9407         9413         9424 
## 1.426783e-05 1.283902e-03 3.124682e-02 1.361263e-05 3.671491e-05 1.851816e-04 
##         9481         9486         9500         9553         9568         9570 
## 1.292210e-02 1.283902e-03 1.283902e-03 1.252681e-01 1.851816e-04 1.361263e-05 
##         9596         9607         9619         9641         9652         9659 
## 7.865246e-06 3.899759e-07 1.851816e-04 1.361263e-05 1.252681e-01 8.967309e-01 
##         9661         9664         9679         9682         9684         9714 
## 7.473835e-01 1.113006e-05 6.987382e-05 7.473835e-01 1.851816e-04 5.317688e-05 
##         9726         9763         9766         9782         9785         9792 
## 2.337187e-04 2.337187e-04 7.865246e-06 8.048715e-03 7.473835e-01 1.361263e-05 
##         9794         9809         9816         9834         9848         9851 
## 7.473835e-01 7.865246e-06 1.851816e-04 1.851816e-04 1.177450e-01 1.113006e-05 
##         9857         9877         9895         9905         9920        10003 
## 8.441843e-07 7.473835e-01 8.048715e-03 1.851816e-04 7.865246e-06 1.851816e-04 
##        10012        10054        10105        10110        10117        10118 
## 1.851816e-04 1.139098e-01 1.876553e-04 3.342656e-05 1.283902e-03 8.048715e-03 
##        10130        10155        10178        10201        10206        10209 
## 7.473835e-01 7.473835e-01 9.947152e-02 7.473835e-01 1.964392e-04 7.473835e-01 
##        10212        10241        10262        10270        10279        10290 
## 1.632376e-06 2.153154e-04 7.865246e-06 7.473835e-01 3.671491e-05 1.851816e-04 
##        10303        10364        10371        10386        10404        10423 
## 1.851816e-04 1.955626e-04 7.473835e-01 1.980591e-04 9.656638e-02 1.361263e-05 
##        10439        10449        10475        10480        10487        10500 
## 1.851816e-04 8.309411e-02 7.784107e-07 1.361263e-05 1.851816e-04 7.473835e-01 
##        10512        10516        10527        10544        10549        10568 
## 1.292210e-02 3.124682e-02 7.473835e-01 8.309411e-02 1.851816e-04 8.309411e-02 
##        10572        10582        10590        10638        10650        10694 
## 1.851816e-04 1.361263e-05 8.309411e-02 5.188210e-04 7.753625e-01 3.124682e-02 
##        10708        10724        10730        10736        10759        10771 
## 1.384216e-02 3.671491e-05 7.473835e-01 1.851816e-04 7.473835e-01 1.292210e-02 
##        10774        10776        10782        10802        10808        10836 
## 7.473835e-01 1.113006e-05 1.283902e-03 7.473835e-01 1.851816e-04 8.568722e-03 
##        10862        10874        10882        10886        10891        10906 
## 7.473835e-01 1.252681e-01 8.309411e-02 5.317688e-05 2.464828e-05 7.473835e-01 
##        10920        10929        10944        10952        10974        10995 
## 8.309411e-02 7.473835e-01 7.473835e-01 7.865246e-06 8.693217e-01 1.851816e-04 
##        11011        11025        11044        11073        11074        11123 
## 7.865246e-06 1.851816e-04 1.292210e-02 6.393403e-03 8.309411e-02 1.113006e-05 
##        11132        11142        11146        11156        11164        11171 
## 1.283902e-03 1.113006e-05 7.473835e-01 3.094893e-02 4.415451e-04 3.094893e-02 
##        11178        11217        11225        11234        11257        11296 
## 1.361263e-05 1.851816e-04 7.473835e-01 1.000000e+00 7.473835e-01 1.851816e-04 
##        11302        11305        11342        11352        11388        11390 
## 1.384216e-02 1.361263e-05 3.236004e-05 3.671491e-05 3.342656e-05 7.473835e-01 
##        11396        11417        11443        11456        11457        11461 
## 5.317688e-05 1.851816e-04 3.124682e-02 9.087979e-03 1.632376e-06 7.570669e-08 
##        11504        11527        11559        11560        11592        11606 
## 7.865246e-06 1.283902e-03 8.309411e-02 1.851816e-04 1.252681e-01 7.473835e-01 
##        11608        11642        11664        11671        11678        11700 
## 8.310226e-02 7.473835e-01 1.283902e-03 1.851816e-04 1.361263e-05 7.473835e-01 
##        11704        11707        11728        11729        11735        11753 
## 7.473835e-01 8.273087e-01 1.892283e-05 2.829945e-02 8.693217e-01 1.113006e-05 
##        11757        11818        11820        11839        11843        11859 
## 7.473835e-01 1.283902e-03 1.361263e-05 1.283902e-03 3.342656e-05 8.309411e-02 
##        11862        11887        11896        11935        11980        11988 
## 1.283902e-03 2.177805e-04 1.851816e-04 7.473835e-01 1.384216e-02 7.473835e-01 
##        12016        12030        12032        12049        12051        12075 
## 8.309411e-02 7.473835e-01 1.851816e-04 8.309411e-02 3.342656e-05 1.851816e-04 
##        12084        12091        12109        12114        12117        12128 
## 1.851816e-04 7.473835e-01 2.050135e-04 1.283902e-03 3.671491e-05 5.317688e-05 
##        12147        12160        12166        12190        12216        12236 
## 8.693217e-01 1.283902e-03 8.568722e-03 1.851816e-04 8.693217e-01 8.309411e-02 
##        12283        12307        12335        12367        12372        12376 
## 1.252681e-01 3.342656e-05 8.693217e-01 1.851816e-04 5.317688e-05 1.851816e-04 
##        12380        12382        12389        12395        12397        12408 
## 8.309411e-02 3.671491e-05 1.252681e-01 1.252681e-01 8.309411e-02 7.473835e-01 
##        12427        12439        12450        12452        12465        12468 
## 1.851816e-04 9.087979e-03 1.283902e-03 1.283902e-03 7.473835e-01 1.361263e-05 
##        12490        12496        12522        12527        12528        12537 
## 8.309411e-02 8.309411e-02 7.865246e-06 1.113006e-05 7.473835e-01 7.473835e-01 
##        12546        12550        12552        12554        12561        12568 
## 7.865246e-06 1.851816e-04 1.851816e-04 1.384216e-02 9.656638e-02 1.851816e-04 
##        12570        12579        12593        12607        12609        12622 
## 7.473835e-01 7.473835e-01 3.124682e-02 7.473835e-01 1.851816e-04 3.671491e-05 
##        12648        12705        12707        12739        12751        12761 
## 1.851816e-04 1.283902e-03 8.693217e-01 2.829945e-02 1.283902e-03 1.490503e-02 
##        12782        12799        12804        12806        12816        12843 
## 1.283902e-03 7.473835e-01 7.865246e-06 7.473835e-01 3.192423e-06 3.671491e-05 
##        12887        12888        12894        12901        12906        12918 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.923103e-04 7.473835e-01 3.671491e-05 
##        12933        12943        12948        12956        12964        12968 
## 1.363611e-05 1.113006e-05 2.337187e-04 9.947152e-02 1.283902e-03 7.473835e-01 
##        12980        12984        13000        13035        13052        13087 
## 1.851816e-04 7.473835e-01 8.693217e-01 7.473835e-01 1.283902e-03 1.716172e-01 
##        13092        13104        13111        13133        13136        13137 
## 1.851816e-04 1.851816e-04 8.309411e-02 1.851816e-04 1.415560e-01 1.283902e-03 
##        13138        13143        13150        13154        13159        13188 
## 1.384216e-02 7.473835e-01 1.292210e-02 1.361263e-05 1.851816e-04 7.473835e-01 
##        13252        13261        13263        13284        13335        13336 
## 7.473835e-01 1.851816e-04 6.393403e-03 1.361263e-05 1.361263e-05 7.473835e-01 
##        13341        13360        13396        13450        13469        13497 
## 1.851816e-04 8.309411e-02 7.473835e-01 7.473835e-01 3.192423e-06 1.361263e-05 
##        13540        13553        13565        13586        13602        13621 
## 1.876553e-04 1.851816e-04 1.384216e-02 7.865246e-06 8.309411e-02 1.361263e-05 
##        13635        13636        13647        13656        13660        13674 
## 1.632376e-06 1.292210e-02 7.473835e-01 1.361263e-05 3.671491e-05 7.473835e-01 
##        13675        13682        13690        13732        13737        13742 
## 7.473835e-01 1.283902e-03 1.361263e-05 7.473835e-01 3.342656e-05 8.309411e-02 
##        13753        13755        13761        13777        13778        13782 
## 7.473835e-01 1.851816e-04 1.851816e-04 2.051463e-04 1.384216e-02 8.309411e-02 
##        13784        13791        13807        13892        13916        13962 
## 1.851816e-04 1.283902e-03 7.473835e-01 7.473835e-01 1.077222e-03 7.473835e-01 
##        13967        13989        14009        14035        14037        14060 
## 1.851816e-04 1.851816e-04 1.113006e-05 7.473835e-01 1.851816e-04 1.851816e-04 
##        14061        14064        14085        14095        14104        14110 
## 1.252681e-01 9.087979e-03 7.473835e-01 8.309411e-02 5.317688e-05 7.865246e-06 
##        14118        14119        14122        14125        14135        14137 
## 1.361263e-05 2.177740e-04 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 
##        14158        14187        14203        14204        14210        14216 
## 7.865246e-06 1.851816e-04 8.309411e-02 1.440165e-05 7.473835e-01 3.342656e-05 
##        14221        14256        14305        14311        14318        14321 
## 7.865246e-06 8.568722e-03 7.473835e-01 9.095206e-03 7.473835e-01 1.851816e-04 
##        14346        14358        14362        14368        14374        14403 
## 2.402165e-01 8.309411e-02 1.851816e-04 1.851816e-04 1.283902e-03 1.851816e-04 
##        14404        14414        14422        14435        14443        14481 
## 9.479464e-01 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.283902e-03 
##        14543        14571        14581        14592        14609        14628 
## 7.473835e-01 8.048715e-03 1.252681e-01 7.473835e-01 8.406202e-07 7.473835e-01 
##        14633        14635        14664        14683        14692        14725 
## 3.671491e-05 8.309411e-02 7.473835e-01 5.317688e-05 8.309411e-02 1.851816e-04 
##        14741        14743        14747        14751        14762        14780 
## 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 8.693217e-01 1.851816e-04 
##        14781        14787        14817        14819        14860        14895 
## 4.817649e-04 7.473835e-01 1.283902e-03 1.851816e-04 5.317688e-05 7.865246e-06 
##        14907        14925        14945        14947        14955        14963 
## 7.473835e-01 1.851816e-04 7.473835e-01 3.124682e-02 1.361263e-05 2.139593e-05 
##        15005        15024        15037        15096        15134        15143 
## 2.674842e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.865246e-06 1.415560e-01 
##        15194        15196        15200        15217        15220        15242 
## 8.309411e-02 3.671491e-05 7.865246e-06 6.987382e-05 1.361263e-05 3.342656e-05 
##        15249 
## 7.473835e-01
hist(authority, labels = TRUE, ylim = c(0,800), xlim = c(0,1), xlab = "Authority Score", main = "Histograma de los Valores de Authority Score")

Cuales son los usuarios con authority score mayor a 0.8:

which(authority >= 0.8)
##   134   679  1175  1467  1833  2316  2329  2426  2427  2660  2846  3009  3200 
##    15    56    90   110   130   157   158   169   170   194   206   217   236 
##  3265  3516  4010  4730  5049  5714  5846  5920  5996  6630  6815  6869  8123 
##   239   259   289   331   360   404   409   423   430   472   482   486   576 
##  8992  9098  9659 10974 11234 11707 11735 12147 12216 12335 12707 13000 14404 
##   630   638   672   761   778   806   809   835   839   843   879   903   997 
## 14762 
##  1019
colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_authority = authority *1000000 + 1
colors <- colorfunc(max(scaled_authority))
V(users_projected)$color <- colors[scaled_authority]

V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = format(round(authority, 2), nsmall = 1),
     vertex.label.color = "Black",
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Usuarios: Nodos según Authority Score")

plot(users_projected, 
     vertex.label = NA,
     vertex.label.color = "Black",
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Usuarios: Nodos según Authority Score")

Hubs

hubs = hub.score(users_projected)$vector
hubs
##           10           11           41           51          114           67 
## 1.851816e-04 1.283902e-03 3.094893e-02 8.309411e-02 8.051461e-03 7.473835e-01 
##           78           82           85           98          107          128 
## 1.361263e-05 1.320908e-03 3.240013e-04 7.473835e-01 1.851816e-04 5.317688e-05 
##          132          133          134          143          144          169 
## 1.632376e-06 8.568722e-03 8.693217e-01 1.384216e-02 3.094893e-02 1.851816e-04 
##          182          187          189          203          231          234 
## 1.252681e-01 7.865246e-06 7.473835e-01 8.309411e-02 8.309411e-02 1.851816e-04 
##          246          254          257          258          281          306 
## 1.361263e-05 1.506834e-02 1.283902e-03 1.955626e-04 7.473835e-01 7.865246e-06 
##          345          349          354          376          393          398 
## 1.283902e-03 1.283902e-03 7.473835e-01 3.124682e-02 1.113006e-05 1.283902e-03 
##          448          456          466          470          471          478 
## 7.473835e-01 1.632376e-06 2.210498e-04 7.473835e-01 1.292210e-02 8.309411e-02 
##          499          519          521          522          529          533 
## 1.283902e-03 2.829945e-02 8.309411e-02 1.716172e-01 8.309411e-02 1.283902e-03 
##          568          595          620          639          648          656 
## 2.177740e-04 3.192423e-06 7.473835e-01 1.283902e-03 3.124682e-02 1.851816e-04 
##          657          679          697          743          771          796 
## 3.914832e-02 8.693217e-01 1.361263e-05 1.384216e-02 1.716172e-01 1.283902e-03 
##          822          837          838          840          841          859 
## 1.283902e-03 1.384216e-02 3.671491e-05 7.473835e-01 1.632376e-06 8.309411e-02 
##          861          873          917          940          946          948 
## 1.283902e-03 1.283902e-03 7.473835e-01 2.196020e-01 1.283902e-03 1.292210e-02 
##          968          973          976          994         1000         1002 
## 1.376629e-01 1.851816e-04 7.865246e-06 7.473835e-01 7.473835e-01 1.252681e-01 
##         1024         1031         1032         1039         1055         1076 
## 1.851816e-04 3.671491e-05 5.317688e-05 1.851816e-04 1.384216e-02 7.473835e-01 
##         1102         1110         1138         1163         1172         1175 
## 1.851816e-04 9.947152e-02 1.851816e-04 1.923103e-04 1.851816e-04 8.693217e-01 
##         1209         1214         1218         1223         1224         1257 
## 8.309411e-02 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 1.851816e-04 
##         1258         1280         1307         1313         1329         1362 
## 7.865246e-06 1.851816e-04 1.147608e-05 1.252681e-01 1.851816e-04 8.051461e-03 
##         1412         1415         1416         1424         1429         1445 
## 7.473835e-01 8.309411e-02 7.473835e-01 8.309411e-02 3.094893e-02 3.124682e-02 
##         1462         1467         1481         1483         1494         1507 
## 3.094893e-02 8.693217e-01 8.309411e-02 3.671491e-05 1.252681e-01 7.473835e-01 
##         1544         1559         1596         1598         1639         1657 
## 1.716172e-01 1.016310e-01 7.473835e-01 3.094893e-02 1.361263e-05 8.568722e-03 
##         1660         1705         1709         1718         1739         1752 
## 7.473835e-01 1.851816e-04 8.309411e-02 5.977311e-06 1.361263e-05 8.309411e-02 
##         1760         1790         1826         1833         1849         1884 
## 1.361263e-05 1.283902e-03 4.206519e-05 8.273087e-01 7.473835e-01 1.361263e-05 
##         1898         1902         1924         1933         1984         1994 
## 1.716172e-01 8.309411e-02 1.283902e-03 1.851816e-04 1.851816e-04 1.851816e-04 
##         2001         2011         2019         2026         2042         2063 
## 1.283902e-03 1.361263e-05 7.865246e-06 7.473835e-01 6.573193e-03 5.317688e-05 
##         2084         2129         2143         2149         2188         2192 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 9.183034e-02 1.283902e-03 
##         2193         2199         2227         2250         2286         2293 
## 7.473835e-01 3.671491e-05 2.177740e-04 5.317688e-05 1.851816e-04 8.309411e-02 
##         2316         2329         2330         2335         2349         2350 
## 8.693217e-01 8.693217e-01 1.283902e-03 1.361263e-05 1.252681e-01 7.473835e-01 
##         2377         2380         2388         2393         2405         2415 
## 3.124682e-02 7.473835e-01 1.851816e-04 1.361263e-05 1.384216e-02 8.309411e-02 
##         2426         2427         2460         2462         2466         2471 
## 9.484796e-01 9.216813e-01 3.671491e-05 7.473835e-01 1.292210e-02 7.473835e-01 
##         2484         2491         2492         2502         2504         2516 
## 1.851816e-04 1.252681e-01 1.851816e-04 1.851816e-04 8.309411e-02 7.865246e-06 
##         2524         2526         2527         2533         2542         2549 
## 1.361263e-05 1.892283e-05 7.473835e-01 3.899759e-07 7.473835e-01 1.851816e-04 
##         2557         2562         2582         2596         2601         2603 
## 5.317688e-05 9.183034e-02 1.632376e-06 2.205150e-01 1.851816e-04 8.309411e-02 
##         2623         2660         2663         2701         2720         2730 
## 1.113006e-05 8.693217e-01 1.951956e-01 1.113006e-05 7.865246e-06 1.283902e-03 
##         2738         2795         2806         2811         2820         2835 
## 1.283902e-03 7.473835e-01 6.423139e-04 7.473835e-01 1.534919e-06 7.473835e-01 
##         2844         2846         2849         2861         2872         2876 
## 7.473835e-01 8.693217e-01 7.473835e-01 8.568722e-03 4.415451e-04 8.309411e-02 
##         2908         2920         2951         2961         2986         2987 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.361263e-05 8.309411e-02 1.113006e-05 
##         3009         3020         3029         3051         3058         3065 
## 8.693217e-01 1.252681e-01 7.473835e-01 1.851816e-04 1.283902e-03 7.473835e-01 
##         3066         3091         3103         3119         3134         3136 
## 1.851816e-04 7.473835e-01 1.113006e-05 7.473835e-01 1.384216e-02 7.865246e-06 
##         3137         3150         3152         3158         3167         3186 
## 1.292210e-02 7.473835e-01 8.318815e-05 2.075671e-01 1.113006e-05 7.473835e-01 
##         3187         3200         3230         3260         3265         3278 
## 1.441853e-01 8.788411e-01 1.851816e-04 3.859943e-03 8.967309e-01 1.283902e-03 
##         3298         3314         3327         3345         3350         3356 
## 7.473835e-01 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 3.342656e-05 
##         3384         3397         3401         3404         3408         3411 
## 7.473835e-01 9.679743e-02 7.865246e-06 1.361263e-05 7.473835e-01 1.361263e-05 
##         3443         3459         3461         3469         3491         3505 
## 7.473835e-01 7.473835e-01 3.192423e-06 8.309411e-02 3.671491e-05 1.283902e-03 
##         3516         3519         3533         3549         3554         3557 
## 8.551731e-01 2.177740e-04 1.851816e-04 7.865246e-06 8.309411e-02 7.473835e-01 
##         3571         3577         3595         3596         3635         3648 
## 1.851816e-04 1.361263e-05 1.361263e-05 8.309411e-02 1.252681e-01 7.473835e-01 
##         3651         3723         3727         3728         3733         3750 
## 8.309411e-02 1.851816e-04 2.464828e-05 8.309411e-02 3.342656e-05 1.851816e-04 
##         3752         3753         3790         3833         3845         3857 
## 8.309411e-02 1.252681e-01 1.851816e-04 7.473835e-01 2.829945e-02 1.283902e-03 
##         3873         3893         3940         3965         3987         3989 
## 9.815029e-03 1.851816e-04 1.361263e-05 3.124682e-02 3.671491e-05 1.283902e-03 
##         4010         4011         4014         4068         4070         4080 
## 8.693217e-01 1.113006e-05 7.473835e-01 1.376629e-01 7.473835e-01 3.192423e-06 
##         4081         4102         4124         4159         4214         4229 
## 7.473835e-01 1.851816e-04 5.317688e-05 1.851816e-04 3.124682e-02 7.473835e-01 
##         4243         4245         4273         4276         4303         4304 
## 7.473835e-01 3.124682e-02 7.473835e-01 1.283902e-03 1.851816e-04 8.309411e-02 
##         4310         4323         4350         4352         4369         4374 
## 1.851816e-04 7.473835e-01 3.859943e-03 3.899759e-07 7.473835e-01 3.342656e-05 
##         4384         4432         4461         4470         4472         4476 
## 1.980357e-04 7.473835e-01 5.317688e-05 1.283902e-03 1.851816e-04 1.851816e-04 
##         4489         4526         4536         4542         4550         4590 
## 1.955626e-04 7.473835e-01 1.851816e-04 1.283902e-03 1.632376e-06 1.012641e-02 
##         4600         4615         4633         4667         4705         4708 
## 1.851816e-04 3.124682e-02 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 
##         4730         4750         4751         4756         4760         4792 
## 8.693217e-01 1.851816e-04 3.342656e-05 3.342656e-05 7.473835e-01 8.309411e-02 
##         4800         4801         4820         4822         4823         4833 
## 6.393403e-03 7.865246e-06 8.309411e-02 1.851816e-04 1.632376e-06 1.851816e-04 
##         4843         4846         4862         4864         4875         4879 
## 9.947152e-02 1.851816e-04 1.113006e-05 7.473835e-01 3.342656e-05 5.317688e-05 
##         4890         4904         4910         4921         4930         4954 
## 1.283902e-03 3.671491e-05 7.473835e-01 8.309411e-02 2.089353e-02 3.671491e-05 
##         4964         4982         5014         5015         5044         5049 
## 3.342656e-05 3.671491e-05 3.094893e-02 1.851816e-04 1.113006e-05 8.693217e-01 
##         5055         5057         5072         5103         5115         5120 
## 1.892283e-05 7.473835e-01 7.473835e-01 5.317688e-05 1.716172e-01 8.405604e-02 
##         5132         5136         5146         5179         5189         5223 
## 3.192423e-06 8.980721e-02 1.361263e-05 1.851816e-04 1.361263e-05 7.473835e-01 
##         5231         5251         5292         5293         5327         5331 
## 1.851816e-04 3.124682e-02 3.124682e-02 1.851816e-04 1.851816e-04 1.283902e-03 
##         5342         5359         5423         5424         5438         5446 
## 7.473835e-01 3.671491e-05 7.473835e-01 3.671491e-05 7.473835e-01 1.361263e-05 
##         5453         5461         5466         5507         5508         5531 
## 8.309411e-02 6.393403e-03 1.964649e-04 1.892283e-05 8.385015e-02 7.473835e-01 
##         5547         5552         5554         5556         5564         5579 
## 1.851816e-04 2.210498e-04 1.283902e-03 7.473835e-01 7.865246e-06 8.406202e-07 
##         5583         5597         5624         5666         5670         5688 
## 7.473835e-01 3.342656e-05 1.851816e-04 1.851816e-04 1.851816e-04 1.851816e-04 
##         5707         5714         5726         5731         5771         5793 
## 1.851816e-04 8.693217e-01 7.473835e-01 1.283902e-03 7.473835e-01 1.851816e-04 
##         5846         5849         5867         5881         5886         5899 
## 8.693217e-01 7.473835e-01 1.851816e-04 1.851816e-04 1.292210e-02 1.361263e-05 
##         5901         5902         5904         5905         5906         5911 
## 1.851816e-04 1.851816e-04 1.851816e-04 1.292210e-02 7.473835e-01 8.309411e-02 
##         5912         5918         5920         5939         5948         5962 
## 1.283902e-03 1.851816e-04 8.693217e-01 1.113006e-05 1.361263e-05 1.955626e-04 
##         5965         5973         5994         5996         5999         6003 
## 7.473835e-01 7.473835e-01 1.851816e-04 9.221897e-01 1.113006e-05 1.851816e-04 
##         6009         6018         6022         6054         6078         6085 
## 9.947152e-02 1.980357e-04 3.671491e-05 1.994648e-01 6.987382e-05 1.851816e-04 
##         6118         6121         6125         6134         6145         6163 
## 7.473835e-01 7.473835e-01 8.309411e-02 7.865246e-06 3.342656e-05 7.473835e-01 
##         6169         6173         6190         6202         6221         6223 
## 7.865246e-06 2.829945e-02 1.851816e-04 3.192423e-06 1.283902e-03 7.473835e-01 
##         6258         6322         6336         6345         6349         6350 
## 7.473835e-01 1.283902e-03 1.361263e-05 9.087979e-03 3.671491e-05 7.865246e-06 
##         6354         6367         6370         6373         6391         6404 
## 1.283902e-03 1.851816e-04 1.851816e-04 1.292210e-02 1.851816e-04 1.283902e-03 
##         6451         6472         6498         6505         6554         6563 
## 7.473835e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 
##         6576         6591         6600         6630         6647         6679 
## 8.309411e-02 1.955626e-04 3.124682e-02 8.273087e-01 9.087979e-03 1.851816e-04 
##         6690         6695         6742         6757         6764         6784 
## 7.865246e-06 1.851816e-04 7.473835e-01 7.473835e-01 1.283902e-03 1.955626e-04 
##         6785         6815         6821         6857         6860         6869 
## 1.851816e-04 9.728658e-01 7.473835e-01 3.671491e-05 7.473835e-01 8.693217e-01 
##         6876         6880         6901         6914         6918         6920 
## 9.087979e-03 1.923103e-04 1.283902e-03 1.077222e-03 7.570669e-08 7.473835e-01 
##         6938         6939         6943         6946         6949         6955 
## 1.851816e-04 8.051461e-03 1.851816e-04 1.851816e-04 7.473835e-01 8.309411e-02 
##         6962         7026         7041         7048         7082         7103 
## 1.955626e-04 7.473835e-01 1.283902e-03 7.473835e-01 7.473835e-01 7.473835e-01 
##         7109         7116         7129         7137         7194         7202 
## 7.865246e-06 1.113006e-05 7.473835e-01 1.361263e-05 1.851816e-04 7.473835e-01 
##         7242         7261         7277         7295         7313         7316 
## 7.473835e-01 1.851816e-04 9.087979e-03 1.292210e-02 1.283902e-03 1.851816e-04 
##         7335         7337         7345         7352         7367         7373 
## 1.851816e-04 1.384216e-02 1.113006e-05 1.851816e-04 7.473835e-01 1.716172e-01 
##         7375         7392         7397         7398         7401         7430 
## 7.473835e-01 7.473835e-01 1.113006e-05 1.851816e-04 1.283902e-03 3.124682e-02 
##         7456         7458         7461         7472         7480         7482 
## 1.283902e-03 3.671491e-05 8.309411e-02 5.317688e-05 7.473835e-01 1.851816e-04 
##         7483         7508         7514         7564         7566         7569 
## 1.947474e-04 1.851816e-04 7.473835e-01 3.094893e-02 8.309411e-02 1.292577e-02 
##         7578         7619         7623         7624         7649         7697 
## 1.851816e-04 7.473835e-01 7.473835e-01 1.980357e-04 1.361263e-05 1.283902e-03 
##         7718         7731         7746         7756         7762         7765 
## 1.851816e-04 1.851816e-04 3.671491e-05 1.716172e-01 4.206519e-05 8.309411e-02 
##         7772         7779         7825         7830         7837         7850 
## 1.415560e-01 7.473835e-01 3.342656e-05 1.113006e-05 8.309411e-02 1.361263e-05 
##         7859         7862         7887         7890         7902         7904 
## 3.671491e-05 3.342656e-05 1.851816e-04 1.361263e-05 1.252681e-01 7.473835e-01 
##         7905         7941         7962         7964         7966         7983 
## 1.851816e-04 1.851816e-04 3.124682e-02 1.283902e-03 8.309411e-02 1.851816e-04 
##         8006         8015         8030         8077         8113         8123 
## 1.283902e-03 1.851816e-04 3.342656e-05 1.851816e-04 1.851816e-04 8.693217e-01 
##         8133         8134         8168         8174         8181         8183 
## 8.309411e-02 1.177450e-01 3.671491e-05 1.252681e-01 7.865246e-06 1.851816e-04 
##         8208         8220         8223         8253         8267         8293 
## 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.259357e-05 1.851816e-04 
##         8294         8309         8338         8342         8362         8365 
## 7.473835e-01 1.260691e-01 8.309411e-02 1.851816e-04 1.113006e-05 7.865246e-06 
##         8370         8373         8382         8393         8413         8426 
## 6.987382e-05 8.309411e-02 1.851816e-04 1.292210e-02 1.283902e-03 8.309411e-02 
##         8485         8542         8546         8566         8593         8609 
## 7.473835e-01 1.851816e-04 7.473835e-01 8.309411e-02 7.473835e-01 1.716172e-01 
##         8627         8663         8679         8708         8742         8746 
## 3.192423e-06 3.124682e-02 7.865246e-06 3.342656e-05 1.283902e-03 1.252681e-01 
##         8751         8761         8783         8787         8798         8825 
## 2.210498e-04 1.851816e-04 1.292210e-02 1.292210e-02 1.851816e-04 8.309411e-02 
##         8831         8850         8868         8878         8880         8894 
## 1.851816e-04 1.283902e-03 7.473835e-01 2.464828e-05 9.255031e-02 8.309411e-02 
##         8914         8931         8939         8953         8957         8992 
## 3.671491e-05 1.851816e-04 3.671491e-05 1.283902e-03 1.292210e-02 8.693217e-01 
##         8997         9015         9018         9025         9048         9061 
## 8.309411e-02 7.473835e-01 1.534919e-06 7.473835e-01 1.252681e-01 1.292210e-02 
##         9095         9098         9117         9129         9140         9163 
## 1.851816e-04 8.273087e-01 1.851816e-04 2.153154e-04 9.131307e-02 1.113006e-05 
##         9204         9210         9228         9229         9250         9253 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.851816e-04 9.255031e-02 8.309411e-02 
##         9309         9310         9320         9341         9350         9355 
## 3.124682e-02 7.473835e-01 2.829945e-02 7.473835e-01 8.309411e-02 7.473835e-01 
##         9358         9373         9384         9407         9413         9424 
## 1.426783e-05 1.283902e-03 3.124682e-02 1.361263e-05 3.671491e-05 1.851816e-04 
##         9481         9486         9500         9553         9568         9570 
## 1.292210e-02 1.283902e-03 1.283902e-03 1.252681e-01 1.851816e-04 1.361263e-05 
##         9596         9607         9619         9641         9652         9659 
## 7.865246e-06 3.899759e-07 1.851816e-04 1.361263e-05 1.252681e-01 8.967309e-01 
##         9661         9664         9679         9682         9684         9714 
## 7.473835e-01 1.113006e-05 6.987382e-05 7.473835e-01 1.851816e-04 5.317688e-05 
##         9726         9763         9766         9782         9785         9792 
## 2.337187e-04 2.337187e-04 7.865246e-06 8.048715e-03 7.473835e-01 1.361263e-05 
##         9794         9809         9816         9834         9848         9851 
## 7.473835e-01 7.865246e-06 1.851816e-04 1.851816e-04 1.177450e-01 1.113006e-05 
##         9857         9877         9895         9905         9920        10003 
## 8.441843e-07 7.473835e-01 8.048715e-03 1.851816e-04 7.865246e-06 1.851816e-04 
##        10012        10054        10105        10110        10117        10118 
## 1.851816e-04 1.139098e-01 1.876553e-04 3.342656e-05 1.283902e-03 8.048715e-03 
##        10130        10155        10178        10201        10206        10209 
## 7.473835e-01 7.473835e-01 9.947152e-02 7.473835e-01 1.964392e-04 7.473835e-01 
##        10212        10241        10262        10270        10279        10290 
## 1.632376e-06 2.153154e-04 7.865246e-06 7.473835e-01 3.671491e-05 1.851816e-04 
##        10303        10364        10371        10386        10404        10423 
## 1.851816e-04 1.955626e-04 7.473835e-01 1.980591e-04 9.656638e-02 1.361263e-05 
##        10439        10449        10475        10480        10487        10500 
## 1.851816e-04 8.309411e-02 7.784107e-07 1.361263e-05 1.851816e-04 7.473835e-01 
##        10512        10516        10527        10544        10549        10568 
## 1.292210e-02 3.124682e-02 7.473835e-01 8.309411e-02 1.851816e-04 8.309411e-02 
##        10572        10582        10590        10638        10650        10694 
## 1.851816e-04 1.361263e-05 8.309411e-02 5.188210e-04 7.753625e-01 3.124682e-02 
##        10708        10724        10730        10736        10759        10771 
## 1.384216e-02 3.671491e-05 7.473835e-01 1.851816e-04 7.473835e-01 1.292210e-02 
##        10774        10776        10782        10802        10808        10836 
## 7.473835e-01 1.113006e-05 1.283902e-03 7.473835e-01 1.851816e-04 8.568722e-03 
##        10862        10874        10882        10886        10891        10906 
## 7.473835e-01 1.252681e-01 8.309411e-02 5.317688e-05 2.464828e-05 7.473835e-01 
##        10920        10929        10944        10952        10974        10995 
## 8.309411e-02 7.473835e-01 7.473835e-01 7.865246e-06 8.693217e-01 1.851816e-04 
##        11011        11025        11044        11073        11074        11123 
## 7.865246e-06 1.851816e-04 1.292210e-02 6.393403e-03 8.309411e-02 1.113006e-05 
##        11132        11142        11146        11156        11164        11171 
## 1.283902e-03 1.113006e-05 7.473835e-01 3.094893e-02 4.415451e-04 3.094893e-02 
##        11178        11217        11225        11234        11257        11296 
## 1.361263e-05 1.851816e-04 7.473835e-01 1.000000e+00 7.473835e-01 1.851816e-04 
##        11302        11305        11342        11352        11388        11390 
## 1.384216e-02 1.361263e-05 3.236004e-05 3.671491e-05 3.342656e-05 7.473835e-01 
##        11396        11417        11443        11456        11457        11461 
## 5.317688e-05 1.851816e-04 3.124682e-02 9.087979e-03 1.632376e-06 7.570669e-08 
##        11504        11527        11559        11560        11592        11606 
## 7.865246e-06 1.283902e-03 8.309411e-02 1.851816e-04 1.252681e-01 7.473835e-01 
##        11608        11642        11664        11671        11678        11700 
## 8.310226e-02 7.473835e-01 1.283902e-03 1.851816e-04 1.361263e-05 7.473835e-01 
##        11704        11707        11728        11729        11735        11753 
## 7.473835e-01 8.273087e-01 1.892283e-05 2.829945e-02 8.693217e-01 1.113006e-05 
##        11757        11818        11820        11839        11843        11859 
## 7.473835e-01 1.283902e-03 1.361263e-05 1.283902e-03 3.342656e-05 8.309411e-02 
##        11862        11887        11896        11935        11980        11988 
## 1.283902e-03 2.177805e-04 1.851816e-04 7.473835e-01 1.384216e-02 7.473835e-01 
##        12016        12030        12032        12049        12051        12075 
## 8.309411e-02 7.473835e-01 1.851816e-04 8.309411e-02 3.342656e-05 1.851816e-04 
##        12084        12091        12109        12114        12117        12128 
## 1.851816e-04 7.473835e-01 2.050135e-04 1.283902e-03 3.671491e-05 5.317688e-05 
##        12147        12160        12166        12190        12216        12236 
## 8.693217e-01 1.283902e-03 8.568722e-03 1.851816e-04 8.693217e-01 8.309411e-02 
##        12283        12307        12335        12367        12372        12376 
## 1.252681e-01 3.342656e-05 8.693217e-01 1.851816e-04 5.317688e-05 1.851816e-04 
##        12380        12382        12389        12395        12397        12408 
## 8.309411e-02 3.671491e-05 1.252681e-01 1.252681e-01 8.309411e-02 7.473835e-01 
##        12427        12439        12450        12452        12465        12468 
## 1.851816e-04 9.087979e-03 1.283902e-03 1.283902e-03 7.473835e-01 1.361263e-05 
##        12490        12496        12522        12527        12528        12537 
## 8.309411e-02 8.309411e-02 7.865246e-06 1.113006e-05 7.473835e-01 7.473835e-01 
##        12546        12550        12552        12554        12561        12568 
## 7.865246e-06 1.851816e-04 1.851816e-04 1.384216e-02 9.656638e-02 1.851816e-04 
##        12570        12579        12593        12607        12609        12622 
## 7.473835e-01 7.473835e-01 3.124682e-02 7.473835e-01 1.851816e-04 3.671491e-05 
##        12648        12705        12707        12739        12751        12761 
## 1.851816e-04 1.283902e-03 8.693217e-01 2.829945e-02 1.283902e-03 1.490503e-02 
##        12782        12799        12804        12806        12816        12843 
## 1.283902e-03 7.473835e-01 7.865246e-06 7.473835e-01 3.192423e-06 3.671491e-05 
##        12887        12888        12894        12901        12906        12918 
## 7.473835e-01 7.473835e-01 1.851816e-04 1.923103e-04 7.473835e-01 3.671491e-05 
##        12933        12943        12948        12956        12964        12968 
## 1.363611e-05 1.113006e-05 2.337187e-04 9.947152e-02 1.283902e-03 7.473835e-01 
##        12980        12984        13000        13035        13052        13087 
## 1.851816e-04 7.473835e-01 8.693217e-01 7.473835e-01 1.283902e-03 1.716172e-01 
##        13092        13104        13111        13133        13136        13137 
## 1.851816e-04 1.851816e-04 8.309411e-02 1.851816e-04 1.415560e-01 1.283902e-03 
##        13138        13143        13150        13154        13159        13188 
## 1.384216e-02 7.473835e-01 1.292210e-02 1.361263e-05 1.851816e-04 7.473835e-01 
##        13252        13261        13263        13284        13335        13336 
## 7.473835e-01 1.851816e-04 6.393403e-03 1.361263e-05 1.361263e-05 7.473835e-01 
##        13341        13360        13396        13450        13469        13497 
## 1.851816e-04 8.309411e-02 7.473835e-01 7.473835e-01 3.192423e-06 1.361263e-05 
##        13540        13553        13565        13586        13602        13621 
## 1.876553e-04 1.851816e-04 1.384216e-02 7.865246e-06 8.309411e-02 1.361263e-05 
##        13635        13636        13647        13656        13660        13674 
## 1.632376e-06 1.292210e-02 7.473835e-01 1.361263e-05 3.671491e-05 7.473835e-01 
##        13675        13682        13690        13732        13737        13742 
## 7.473835e-01 1.283902e-03 1.361263e-05 7.473835e-01 3.342656e-05 8.309411e-02 
##        13753        13755        13761        13777        13778        13782 
## 7.473835e-01 1.851816e-04 1.851816e-04 2.051463e-04 1.384216e-02 8.309411e-02 
##        13784        13791        13807        13892        13916        13962 
## 1.851816e-04 1.283902e-03 7.473835e-01 7.473835e-01 1.077222e-03 7.473835e-01 
##        13967        13989        14009        14035        14037        14060 
## 1.851816e-04 1.851816e-04 1.113006e-05 7.473835e-01 1.851816e-04 1.851816e-04 
##        14061        14064        14085        14095        14104        14110 
## 1.252681e-01 9.087979e-03 7.473835e-01 8.309411e-02 5.317688e-05 7.865246e-06 
##        14118        14119        14122        14125        14135        14137 
## 1.361263e-05 2.177740e-04 7.473835e-01 7.473835e-01 7.473835e-01 1.851816e-04 
##        14158        14187        14203        14204        14210        14216 
## 7.865246e-06 1.851816e-04 8.309411e-02 1.440165e-05 7.473835e-01 3.342656e-05 
##        14221        14256        14305        14311        14318        14321 
## 7.865246e-06 8.568722e-03 7.473835e-01 9.095206e-03 7.473835e-01 1.851816e-04 
##        14346        14358        14362        14368        14374        14403 
## 2.402165e-01 8.309411e-02 1.851816e-04 1.851816e-04 1.283902e-03 1.851816e-04 
##        14404        14414        14422        14435        14443        14481 
## 9.479464e-01 1.851816e-04 7.473835e-01 7.473835e-01 3.671491e-05 1.283902e-03 
##        14543        14571        14581        14592        14609        14628 
## 7.473835e-01 8.048715e-03 1.252681e-01 7.473835e-01 8.406202e-07 7.473835e-01 
##        14633        14635        14664        14683        14692        14725 
## 3.671491e-05 8.309411e-02 7.473835e-01 5.317688e-05 8.309411e-02 1.851816e-04 
##        14741        14743        14747        14751        14762        14780 
## 1.851816e-04 7.473835e-01 1.851816e-04 7.473835e-01 8.693217e-01 1.851816e-04 
##        14781        14787        14817        14819        14860        14895 
## 4.817649e-04 7.473835e-01 1.283902e-03 1.851816e-04 5.317688e-05 7.865246e-06 
##        14907        14925        14945        14947        14955        14963 
## 7.473835e-01 1.851816e-04 7.473835e-01 3.124682e-02 1.361263e-05 2.139593e-05 
##        15005        15024        15037        15096        15134        15143 
## 2.674842e-01 1.851816e-04 1.851816e-04 7.473835e-01 7.865246e-06 1.415560e-01 
##        15194        15196        15200        15217        15220        15242 
## 8.309411e-02 3.671491e-05 7.865246e-06 6.987382e-05 1.361263e-05 3.342656e-05 
##        15249 
## 7.473835e-01
hist(hubs, labels = TRUE, ylim = c(0,800), xlim = c(0,1), xlab = "Hub Score", main = "Histograma de los Valores de Hub Score")

Cuales son los usuarios con alto hub score:

which(hubs >= 0.8)
##   134   679  1175  1467  1833  2316  2329  2426  2427  2660  2846  3009  3200 
##    15    56    90   110   130   157   158   169   170   194   206   217   236 
##  3265  3516  4010  4730  5049  5714  5846  5920  5996  6630  6815  6869  8123 
##   239   259   289   331   360   404   409   423   430   472   482   486   576 
##  8992  9098  9659 10974 11234 11707 11735 12147 12216 12335 12707 13000 14404 
##   630   638   672   761   778   806   809   835   839   843   879   903   997 
## 14762 
##  1019
colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_hubs = hubs * 1000000 + 1
colors <- colorfunc(max(scaled_hubs))
V(users_projected)$color <- colors[scaled_hubs]

V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = format(round(hubs, 2), nsmall = 1),
     vertex.label.color = "Black",
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Usuarios: Nodos según Hub Score")

plot(users_projected, 
     vertex.label = NA,
     vertex.label.color = "Black",
     vertex.size = 3,
     edge.arrow.size=0.1,
     layout = layout_components,
     main = "Proyección Red Usuarios: Nodos según Hub Score")

Medidas de Centralidad Basadas en Caminos más Cortos

Closeness Centrality

closeness_centrality = closeness(users_projected)
closeness_centrality
##           10           11           41           51          114           67 
## 0.0003838772 0.0002992220 0.0003567606 0.0003933910 0.0003539823 0.0003875969 
##           78           82           85           98          107          128 
## 0.0003176620 0.0003001200 0.0003620565 0.0003875969 0.0003838772 0.0002642706 
##          132          133          134          143          144          169 
## 0.0002843332 0.0003601008 0.0003998401 0.0003639010 0.0003567606 0.0003838772 
##          182          187          189          203          231          234 
## 0.0003714710 0.0002913753 0.0003875969 0.0003933910 0.0003933910 0.0003838772 
##          246          254          257          258          281          306 
## 0.0003176620 0.0003779289 0.0002986858 0.0003903201 0.0003875969 0.0002913753 
##          345          349          354          376          393          398 
## 0.0002986858 0.0002986858 0.0003875969 0.0003610108 0.0002922268 0.0002986858 
##          448          456          466          470          471          478 
## 0.0003875969 0.0002843332 0.0003408316 0.0003875969 0.0003577818 0.0003933910 
##          499          519          521          522          529          533 
## 0.0002986858 0.0003575259 0.0003933910 0.0003941663 0.0003933910 0.0002986858 
##          568          595          620          639          648          656 
## 0.0003359086 0.0002856327 0.0003875969 0.0002986858 0.0003610108 0.0003838772 
##          657          679          697          743          771          796 
## 0.0003627131 0.0003998401 0.0003176620 0.0003639010 0.0003941663 0.0002986858 
##          822          837          838          840          841          859 
## 0.0002986858 0.0003639010 0.0003498950 0.0003875969 0.0002843332 0.0003933910 
##          861          873          917          940          946          948 
## 0.0002986858 0.0002986858 0.0003875969 0.0004050223 0.0002986858 0.0003581662 
##          968          973          976          994         1000         1002 
## 0.0003772161 0.0003838772 0.0002913753 0.0003875969 0.0003875969 0.0003714710 
##         1024         1031         1032         1039         1055         1076 
## 0.0003838772 0.0003498950 0.0002642706 0.0003838772 0.0003639010 0.0003875969 
##         1102         1110         1138         1163         1172         1175 
## 0.0003838772 0.0003920031 0.0003838772 0.0003938558 0.0003838772 0.0003998401 
##         1209         1214         1218         1223         1224         1257 
## 0.0003935458 0.0003838772 0.0003875969 0.0003838772 0.0003875969 0.0003838772 
##         1258         1280         1307         1313         1329         1362 
## 0.0002913753 0.0003838772 0.0002968240 0.0003714710 0.0003838772 0.0003539823 
##         1412         1415         1416         1424         1429         1445 
## 0.0003875969 0.0003935458 0.0003875969 0.0003935458 0.0003567606 0.0003610108 
##         1462         1467         1481         1483         1494         1507 
## 0.0003567606 0.0003998401 0.0003935458 0.0003498950 0.0003714710 0.0003875969 
##         1544         1559         1596         1598         1639         1657 
## 0.0003941663 0.0004633920 0.0003875969 0.0003567606 0.0003176620 0.0003601008 
##         1660         1705         1709         1718         1739         1752 
## 0.0003875969 0.0003838772 0.0003933910 0.0002958580 0.0003176620 0.0003933910 
##         1760         1790         1826         1833         1849         1884 
## 0.0003176620 0.0002986858 0.0002726281 0.0004332756 0.0003875969 0.0003176620 
##         1898         1902         1924         1933         1984         1994 
## 0.0003941663 0.0003933910 0.0002986858 0.0003838772 0.0003838772 0.0003838772 
##         2001         2011         2019         2026         2042         2063 
## 0.0002986858 0.0003176620 0.0002913753 0.0003875969 0.0005136107 0.0002642706 
##         2084         2129         2143         2149         2188         2192 
## 0.0003875969 0.0003875969 0.0003875969 0.0003875969 0.0003929273 0.0002986858 
##         2193         2199         2227         2250         2286         2293 
## 0.0003875969 0.0003472222 0.0003386387 0.0002642706 0.0003838772 0.0003933910 
##         2316         2329         2330         2335         2349         2350 
## 0.0004020909 0.0004020909 0.0002986858 0.0003176620 0.0003714710 0.0003875969 
##         2377         2380         2388         2393         2405         2415 
## 0.0003612717 0.0003875969 0.0003838772 0.0003176620 0.0003639010 0.0003933910 
##         2426         2427         2460         2462         2466         2471 
## 0.0004297379 0.0004366812 0.0003472222 0.0003875969 0.0003581662 0.0003875969 
##         2484         2491         2492         2502         2504         2516 
## 0.0003838772 0.0003714710 0.0003838772 0.0003838772 0.0003933910 0.0002913753 
##         2524         2526         2527         2533         2542         2549 
## 0.0003176620 0.0002930832 0.0003875969 0.0002478315 0.0003875969 0.0003838772 
##         2557         2562         2582         2596         2601         2603 
## 0.0002642706 0.0003929273 0.0002843332 0.0004016064 0.0003838772 0.0003933910 
##         2623         2660         2663         2701         2720         2730 
## 0.0002924832 0.0004020909 0.0003787879 0.0002924832 0.0002913753 0.0002986858 
##         2738         2795         2806         2811         2820         2835 
## 0.0002986858 0.0003875969 0.0002977077 0.0003875969 0.0002168727 0.0003875969 
##         2844         2846         2849         2861         2872         2876 
## 0.0003875969 0.0004020909 0.0003875969 0.0003601008 0.0002767783 0.0003933910 
##         2908         2920         2951         2961         2986         2987 
## 0.0003838772 0.0003838772 0.0003612717 0.0003176620 0.0003933910 0.0002924832 
##         3009         3020         3029         3051         3058         3065 
## 0.0004019293 0.0003714710 0.0003875969 0.0003838772 0.0002986858 0.0003875969 
##         3066         3091         3103         3119         3134         3136 
## 0.0003838772 0.0003875969 0.0002924832 0.0003875969 0.0003639010 0.0002913753 
##         3137         3150         3152         3158         3167         3186 
## 0.0003563792 0.0003875969 0.0003273322 0.0004009623 0.0002924832 0.0003875969 
##         3187         3200         3230         3260         3265         3278 
## 0.0003915427 0.0004071661 0.0003838772 0.0002963841 0.0004040404 0.0002986858 
##         3298         3314         3327         3345         3350         3356 
## 0.0003900156 0.0003900156 0.0003900156 0.0003900156 0.0003838772 0.0003471017 
##         3384         3397         3401         3404         3408         3411 
## 0.0003900156 0.0004608295 0.0002913753 0.0003176620 0.0003900156 0.0003176620 
##         3443         3459         3461         3469         3491         3505 
## 0.0003900156 0.0003900156 0.0002853067 0.0003933910 0.0003472222 0.0002986858 
##         3516         3519         3533         3549         3554         3557 
## 0.0004312204 0.0003382950 0.0003838772 0.0002913753 0.0003933910 0.0003900156 
##         3571         3577         3595         3596         3635         3648 
## 0.0003838772 0.0003176620 0.0003176620 0.0003933910 0.0003714710 0.0003900156 
##         3651         3723         3727         3728         3733         3750 
## 0.0003933910 0.0003838772 0.0003243594 0.0003933910 0.0003466205 0.0003838772 
##         3752         3753         3790         3833         3845         3857 
## 0.0003933910 0.0003714710 0.0003838772 0.0003900156 0.0003575259 0.0002986858 
##         3873         3893         3940         3965         3987         3989 
## 0.0003767898 0.0003838772 0.0003176620 0.0003612717 0.0003472222 0.0002987750 
##         4010         4011         4014         4068         4070         4080 
## 0.0004011231 0.0002924832 0.0003900156 0.0003780718 0.0003900156 0.0002853067 
##         4081         4102         4124         4159         4214         4229 
## 0.0003900156 0.0003838772 0.0002642706 0.0003838772 0.0003612717 0.0003900156 
##         4243         4245         4273         4276         4303         4304 
## 0.0003900156 0.0003612717 0.0003900156 0.0002987750 0.0003838772 0.0003933910 
##         4310         4323         4350         4352         4369         4374 
## 0.0003838772 0.0003900156 0.0002963841 0.0002463054 0.0003900156 0.0003466205 
##         4384         4432         4461         4470         4472         4476 
## 0.0003954132 0.0003900156 0.0002642706 0.0002987750 0.0003838772 0.0003838772 
##         4489         4526         4536         4542         4550         4590 
## 0.0003877472 0.0003900156 0.0003838772 0.0002987750 0.0002843332 0.0003557453 
##         4600         4615         4633         4667         4705         4708 
## 0.0003838772 0.0003612717 0.0003900156 0.0003900156 0.0002924832 0.0003838772 
##         4730         4750         4751         4756         4760         4792 
## 0.0004011231 0.0003838772 0.0003466205 0.0003466205 0.0003900156 0.0003933910 
##         4800         4801         4820         4822         4823         4833 
## 0.0004175365 0.0002913753 0.0003933910 0.0003838772 0.0002843332 0.0003838772 
##         4843         4846         4862         4864         4875         4879 
## 0.0003927730 0.0003838772 0.0002924832 0.0003900156 0.0003466205 0.0002642706 
##         4890         4904         4910         4921         4930         4954 
## 0.0002987750 0.0003472222 0.0003900156 0.0003933910 0.0003580380 0.0003472222 
##         4964         4982         5014         5015         5044         5049 
## 0.0003466205 0.0003472222 0.0003557453 0.0003838772 0.0002924832 0.0004011231 
##         5055         5057         5072         5103         5115         5120 
## 0.0002930832 0.0003900156 0.0003900156 0.0002642706 0.0003937008 0.0004060089 
##         5132         5136         5146         5179         5189         5223 
## 0.0002853067 0.0003049710 0.0003176620 0.0003838772 0.0003176620 0.0003900156 
##         5231         5251         5292         5293         5327         5331 
## 0.0003838772 0.0003612717 0.0003612717 0.0003838772 0.0003838772 0.0002987750 
##         5342         5359         5423         5424         5438         5446 
## 0.0003900156 0.0003472222 0.0003900156 0.0003472222 0.0003900156 0.0003176620 
##         5453         5461         5466         5507         5508         5531 
## 0.0003935458 0.0004175365 0.0003935458 0.0002930832 0.0003929273 0.0003900156 
##         5547         5552         5554         5556         5564         5579 
## 0.0003844675 0.0003408316 0.0002987750 0.0003900156 0.0002913753 0.0002508151 
##         5583         5597         5624         5666         5670         5688 
## 0.0003900156 0.0003466205 0.0003844675 0.0003844675 0.0003844675 0.0003844675 
##         5707         5714         5726         5731         5771         5793 
## 0.0003844675 0.0004011231 0.0003900156 0.0002987750 0.0003900156 0.0003844675 
##         5846         5849         5867         5881         5886         5899 
## 0.0004011231 0.0003900156 0.0003844675 0.0003844675 0.0003567606 0.0003176620 
##         5901         5902         5904         5905         5906         5911 
## 0.0003844675 0.0003844675 0.0003844675 0.0003567606 0.0003900156 0.0003935458 
##         5912         5918         5920         5939         5948         5962 
## 0.0002987750 0.0003844675 0.0004011231 0.0002922268 0.0003176620 0.0003866976 
##         5965         5973         5994         5996         5999         6003 
## 0.0003900156 0.0003900156 0.0003844675 0.0004363002 0.0002912056 0.0003844675 
##         6009         6018         6022         6054         6078         6085 
## 0.0003920031 0.0003943218 0.0003472222 0.0003943218 0.0002911208 0.0003844675 
##         6118         6121         6125         6134         6145         6163 
## 0.0003900156 0.0003900156 0.0003935458 0.0002913753 0.0003492840 0.0003900156 
##         6169         6173         6190         6202         6221         6223 
## 0.0002913753 0.0003567606 0.0003844675 0.0002853067 0.0002987750 0.0003900156 
##         6258         6322         6336         6345         6349         6350 
## 0.0003900156 0.0002987750 0.0003176620 0.0003552398 0.0003472222 0.0002913753 
##         6354         6367         6370         6373         6391         6404 
## 0.0002987750 0.0003844675 0.0003844675 0.0003567606 0.0003844675 0.0002987750 
##         6451         6472         6498         6505         6554         6563 
## 0.0003900156 0.0003844675 0.0003844675 0.0003900156 0.0003900156 0.0002987750 
##         6576         6591         6600         6630         6647         6679 
## 0.0003935458 0.0003866976 0.0003612717 0.0004330879 0.0003552398 0.0003844675 
##         6690         6695         6742         6757         6764         6784 
## 0.0002913753 0.0003844675 0.0003900156 0.0003900156 0.0002987750 0.0003866976 
##         6785         6815         6821         6857         6860         6869 
## 0.0003844675 0.0004277160 0.0003900156 0.0003472222 0.0003900156 0.0004008016 
##         6876         6880         6901         6914         6918         6920 
## 0.0003552398 0.0003930818 0.0002987750 0.0002773156 0.0002416043 0.0003901678 
##         6938         6939         6943         6946         6949         6955 
## 0.0003844675 0.0003539823 0.0003844675 0.0003844675 0.0003901678 0.0003933910 
##         6962         7026         7041         7048         7082         7103 
## 0.0003866976 0.0003901678 0.0002987750 0.0003901678 0.0003901678 0.0003901678 
##         7109         7116         7129         7137         7194         7202 
## 0.0002913753 0.0002912056 0.0003901678 0.0003176620 0.0003844675 0.0003901678 
##         7242         7261         7277         7295         7313         7316 
## 0.0003901678 0.0003844675 0.0003552398 0.0003567606 0.0002987750 0.0003844675 
##         7335         7337         7345         7352         7367         7373 
## 0.0003844675 0.0003639010 0.0002912056 0.0003844675 0.0003901678 0.0003938558 
##         7375         7392         7397         7398         7401         7430 
## 0.0003901678 0.0003901678 0.0002912056 0.0003844675 0.0002987750 0.0003612717 
##         7456         7458         7461         7472         7480         7482 
## 0.0002987750 0.0003472222 0.0003933910 0.0002642706 0.0003901678 0.0003844675 
##         7483         7508         7514         7564         7566         7569 
## 0.0003941663 0.0003844675 0.0003901678 0.0003557453 0.0003933910 0.0003607504 
##         7578         7619         7623         7624         7649         7697 
## 0.0003844675 0.0003901678 0.0003901678 0.0003946330 0.0003176620 0.0002987750 
##         7718         7731         7746         7756         7762         7765 
## 0.0003844675 0.0003844675 0.0003472222 0.0003938558 0.0002726281 0.0003933910 
##         7772         7779         7825         7830         7837         7850 
## 0.0003897116 0.0003901678 0.0003492840 0.0002912056 0.0003933910 0.0003176620 
##         7859         7862         7887         7890         7902         7904 
## 0.0003472222 0.0003492840 0.0003844675 0.0003176620 0.0003714710 0.0003901678 
##         7905         7941         7962         7964         7966         7983 
## 0.0003844675 0.0003844675 0.0003612717 0.0002987750 0.0003933910 0.0003844675 
##         8006         8015         8030         8077         8113         8123 
## 0.0002987750 0.0003844675 0.0003492840 0.0003844675 0.0003844675 0.0004011231 
##         8133         8134         8168         8174         8181         8183 
## 0.0003933910 0.0004690432 0.0003472222 0.0003714710 0.0002913753 0.0003844675 
##         8208         8220         8223         8253         8267         8293 
## 0.0003844675 0.0003901678 0.0003901678 0.0003472222 0.0002942908 0.0003844675 
##         8294         8309         8338         8342         8362         8365 
## 0.0003901678 0.0003846154 0.0003933910 0.0003844675 0.0002912056 0.0002913753 
##         8370         8373         8382         8393         8413         8426 
## 0.0002911208 0.0003933910 0.0003844675 0.0003581662 0.0002991325 0.0003933910 
##         8485         8542         8546         8566         8593         8609 
## 0.0003901678 0.0003844675 0.0003901678 0.0003933910 0.0003901678 0.0003938558 
##         8627         8663         8679         8708         8742         8746 
## 0.0002853067 0.0003612717 0.0002913753 0.0003492840 0.0002991325 0.0003714710 
##         8751         8761         8783         8787         8798         8825 
## 0.0003408316 0.0003844675 0.0003581662 0.0003581662 0.0003844675 0.0003933910 
##         8831         8850         8868         8878         8880         8894 
## 0.0003844675 0.0002991325 0.0003901678 0.0003215434 0.0003929273 0.0003935458 
##         8914         8931         8939         8953         8957         8992 
## 0.0003472222 0.0003844675 0.0003472222 0.0002991325 0.0003581662 0.0004011231 
##         8997         9015         9018         9025         9048         9061 
## 0.0003935458 0.0003901678 0.0002168727 0.0003901678 0.0003714710 0.0003581662 
##         9095         9098         9117         9129         9140         9163 
## 0.0003844675 0.0004330879 0.0003844675 0.0003985652 0.0003941663 0.0002912056 
##         9204         9210         9228         9229         9250         9253 
## 0.0003901678 0.0003901678 0.0003844675 0.0003844675 0.0003929273 0.0003935458 
##         9309         9310         9320         9341         9350         9355 
## 0.0003612717 0.0003901678 0.0003567606 0.0003901678 0.0003935458 0.0003901678 
##         9358         9373         9384         9407         9413         9424 
## 0.0002936858 0.0002991325 0.0003612717 0.0003176620 0.0003472222 0.0003844675 
##         9481         9486         9500         9553         9568         9570 
## 0.0003581662 0.0002991325 0.0002991325 0.0003714710 0.0003844675 0.0003176620 
##         9596         9607         9619         9641         9652         9659 
## 0.0002913753 0.0002463054 0.0003844675 0.0003176620 0.0003714710 0.0004033885 
##         9661         9664         9679         9682         9684         9714 
## 0.0003901678 0.0002923977 0.0002911208 0.0003901678 0.0003844675 0.0002633658 
##         9726         9763         9766         9782         9785         9792 
## 0.0003201024 0.0003201024 0.0002913753 0.0003481894 0.0003901678 0.0003173596 
##         9794         9809         9816         9834         9848         9851 
## 0.0003901678 0.0002913753 0.0003844675 0.0003844675 0.0004703669 0.0002923977 
##         9857         9877         9895         9905         9920        10003 
## 0.0002840102 0.0003901678 0.0003481894 0.0003844675 0.0002913753 0.0003844675 
##        10012        10054        10105        10110        10117        10118 
## 0.0003844675 0.0003891051 0.0003898635 0.0003492840 0.0002991325 0.0003481894 
##        10130        10155        10178        10201        10206        10209 
## 0.0003901678 0.0003901678 0.0003929273 0.0003901678 0.0003944773 0.0003901678 
##        10212        10241        10262        10270        10279        10290 
## 0.0002845760 0.0003985652 0.0002922268 0.0003901678 0.0003472222 0.0003844675 
##        10303        10364        10371        10386        10404        10423 
## 0.0003844675 0.0003866976 0.0003901678 0.0003955696 0.0003933910 0.0003173596 
##        10439        10449        10475        10480        10487        10500 
## 0.0003844675 0.0003935458 0.0002805836 0.0003173596 0.0003844675 0.0003901678 
##        10512        10516        10527        10544        10549        10568 
## 0.0003581662 0.0003612717 0.0003901678 0.0003935458 0.0003844675 0.0003935458 
##        10572        10582        10590        10638        10650        10694 
## 0.0003844675 0.0003173596 0.0003935458 0.0004315926 0.0003392130 0.0003612717 
##        10708        10724        10730        10736        10759        10771 
## 0.0003639010 0.0003472222 0.0003901678 0.0003844675 0.0003901678 0.0003581662 
##        10774        10776        10782        10802        10808        10836 
## 0.0003901678 0.0002923977 0.0002991325 0.0003901678 0.0003844675 0.0003601008 
##        10862        10874        10882        10886        10891        10906 
## 0.0003901678 0.0003714710 0.0003935458 0.0002633658 0.0003243594 0.0003901678 
##        10920        10929        10944        10952        10974        10995 
## 0.0003935458 0.0003901678 0.0003901678 0.0002922268 0.0004011231 0.0003844675 
##        11011        11025        11044        11073        11074        11123 
## 0.0002922268 0.0003844675 0.0003581662 0.0004175365 0.0003935458 0.0002923977 
##        11132        11142        11146        11156        11164        11171 
## 0.0002991325 0.0002923977 0.0003901678 0.0003557453 0.0002794857 0.0003557453 
##        11178        11217        11225        11234        11257        11296 
## 0.0003176620 0.0003844675 0.0003901678 0.0004293688 0.0003901678 0.0003844675 
##        11302        11305        11342        11352        11388        11390 
## 0.0003639010 0.0003176620 0.0003276540 0.0003472222 0.0003492840 0.0003901678 
##        11396        11417        11443        11456        11457        11461 
## 0.0002633658 0.0003844675 0.0003612717 0.0003552398 0.0002845760 0.0002416043 
##        11504        11527        11559        11560        11592        11606 
## 0.0002924832 0.0002991325 0.0003935458 0.0003844675 0.0003714710 0.0003901678 
##        11608        11642        11664        11671        11678        11700 
## 0.0004636069 0.0003901678 0.0002991325 0.0003844675 0.0003176620 0.0003901678 
##        11704        11707        11728        11729        11735        11753 
## 0.0003901678 0.0004332756 0.0002943774 0.0003567606 0.0004011231 0.0002925688 
##        11757        11818        11820        11839        11843        11859 
## 0.0003901678 0.0002991325 0.0003176620 0.0002991325 0.0003492840 0.0003937008 
##        11862        11887        11896        11935        11980        11988 
## 0.0002991325 0.0003390980 0.0003844675 0.0003901678 0.0003639010 0.0003901678 
##        12016        12030        12032        12049        12051        12075 
## 0.0003937008 0.0003901678 0.0003844675 0.0003937008 0.0003474635 0.0003844675 
##        12084        12091        12109        12114        12117        12128 
## 0.0003844675 0.0003901678 0.0003944773 0.0002991325 0.0003472222 0.0002633658 
##        12147        12160        12166        12190        12216        12236 
## 0.0004011231 0.0002991325 0.0003601008 0.0003844675 0.0004011231 0.0003937008 
##        12283        12307        12335        12367        12372        12376 
## 0.0003714710 0.0003474635 0.0004011231 0.0003844675 0.0002633658 0.0003844675 
##        12380        12382        12389        12395        12397        12408 
## 0.0003937008 0.0003472222 0.0003714710 0.0003714710 0.0003937008 0.0003901678 
##        12427        12439        12450        12452        12465        12468 
## 0.0003844675 0.0003552398 0.0002991325 0.0002991325 0.0003901678 0.0003176620 
##        12490        12496        12522        12527        12528        12537 
## 0.0003937008 0.0003937008 0.0002924832 0.0002927400 0.0003901678 0.0003901678 
##        12546        12550        12552        12554        12561        12568 
## 0.0002924832 0.0003844675 0.0003844675 0.0003639010 0.0003943218 0.0003844675 
##        12570        12579        12593        12607        12609        12622 
## 0.0003901678 0.0003901678 0.0003612717 0.0003901678 0.0003844675 0.0003472222 
##        12648        12705        12707        12739        12751        12761 
## 0.0003844675 0.0002991325 0.0004011231 0.0003567606 0.0002991325 0.0004347826 
##        12782        12799        12804        12806        12816        12843 
## 0.0002991325 0.0003901678 0.0002924832 0.0003901678 0.0002853067 0.0003472222 
##        12887        12888        12894        12901        12906        12918 
## 0.0003901678 0.0003901678 0.0003844675 0.0003926188 0.0003901678 0.0003472222 
##        12933        12943        12948        12956        12964        12968 
## 0.0003206156 0.0002927400 0.0003220612 0.0003927730 0.0002991325 0.0003901678 
##        12980        12984        13000        13035        13052        13087 
## 0.0003844675 0.0003901678 0.0004011231 0.0003901678 0.0002991325 0.0003930818 
##        13092        13104        13111        13133        13136        13137 
## 0.0003844675 0.0003844675 0.0003937008 0.0003844675 0.0003895598 0.0002991325 
##        13138        13143        13150        13154        13159        13188 
## 0.0003639010 0.0003901678 0.0003581662 0.0003175611 0.0003844675 0.0003901678 
##        13252        13261        13263        13284        13335        13336 
## 0.0003901678 0.0003844675 0.0004175365 0.0003175611 0.0003175611 0.0003901678 
##        13341        13360        13396        13450        13469        13497 
## 0.0003844675 0.0003937008 0.0003901678 0.0003901678 0.0002853067 0.0003175611 
##        13540        13553        13565        13586        13602        13621 
## 0.0003898635 0.0003844675 0.0003639010 0.0002924832 0.0003937008 0.0003175611 
##        13635        13636        13647        13656        13660        13674 
## 0.0002845760 0.0003581662 0.0003901678 0.0003175611 0.0003472222 0.0003901678 
##        13675        13682        13690        13732        13737        13742 
## 0.0003901678 0.0002991325 0.0003175611 0.0003901678 0.0003474635 0.0003937008 
##        13753        13755        13761        13777        13778        13782 
## 0.0003901678 0.0003844675 0.0003844675 0.0003996803 0.0003639010 0.0003937008 
##        13784        13791        13807        13892        13916        13962 
## 0.0003844675 0.0002991325 0.0003901678 0.0003901678 0.0002770083 0.0003901678 
##        13967        13989        14009        14035        14037        14060 
## 0.0003844675 0.0003844675 0.0002927400 0.0003901678 0.0003844675 0.0003844675 
##        14061        14064        14085        14095        14104        14110 
## 0.0003714710 0.0003552398 0.0003901678 0.0003937008 0.0002633658 0.0002912056 
##        14118        14119        14122        14125        14135        14137 
## 0.0003175611 0.0003384095 0.0003901678 0.0003901678 0.0003901678 0.0003844675 
##        14158        14187        14203        14204        14210        14216 
## 0.0002912056 0.0003844675 0.0003937008 0.0003185728 0.0003901678 0.0003474635 
##        14221        14256        14305        14311        14318        14321 
## 0.0002912056 0.0003601008 0.0003901678 0.0003683241 0.0003901678 0.0003844675 
##        14346        14358        14362        14368        14374        14403 
## 0.0004791567 0.0003937008 0.0003844675 0.0003844675 0.0002991325 0.0003844675 
##        14404        14414        14422        14435        14443        14481 
## 0.0005350455 0.0003844675 0.0003903201 0.0003903201 0.0003472222 0.0002991325 
##        14543        14571        14581        14592        14609        14628 
## 0.0003903201 0.0003462604 0.0003713331 0.0003903201 0.0002507523 0.0003903201 
##        14633        14635        14664        14683        14692        14725 
## 0.0003472222 0.0003937008 0.0003903201 0.0002633658 0.0003937008 0.0003844675 
##        14741        14743        14747        14751        14762        14780 
## 0.0003844675 0.0003903201 0.0003844675 0.0003903201 0.0004017678 0.0003844675 
##        14781        14787        14817        14819        14860        14895 
## 0.0002876043 0.0003903201 0.0002991325 0.0003844675 0.0002633658 0.0002912056 
##        14907        14925        14945        14947        14955        14963 
## 0.0003903201 0.0003844675 0.0003903201 0.0003612717 0.0003175611 0.0003244646 
##        15005        15024        15037        15096        15134        15143 
## 0.0003963535 0.0003844675 0.0003844675 0.0003903201 0.0002912056 0.0003904725 
##        15194        15196        15200        15217        15220        15242 
## 0.0003937008 0.0003472222 0.0002912056 0.0002910361 0.0003182686 0.0003471017 
##        15249 
## 0.0003903201
hist(closeness_centrality, labels = TRUE, ylim = c(0,700), xlab = "Closeness Centrality", main = "Histograma de los Valores de Closeness Centrality")

Graficamos a continuación la red de usuarios - usuarios donde cada nodo tiene el tamaño y color asociado a la métrica de closeness calculada anteriormente.

colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_closeness = closeness_centrality * 10000
colors <- colorfunc(max(scaled_closeness))
V(users_projected)$color <- colors[scaled_closeness]

V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = format(round(closeness_centrality, 2), nsmall = 1),
     vertex.size =  closeness_centrality *1000 / 2,
     edge.arrow.size=0.1,
     layout = layout_components,
    main = "Proyección Red Usuarios: Nodos según Closeness Centrality")

plot(users_projected, 
     vertex.label = NA,
     vertex.size =  closeness_centrality *1000 / 2,
     edge.arrow.size=0.1,
     layout = layout_components,
    main = "Proyección Red Usuarios: Nodos según Closeness Centrality")

Betweenness Centrality

betweenness_centrality <- betweenness(users_projected)
betweenness_centrality
##           10           11           41           51          114           67 
## 2.509666e+01 0.000000e+00 1.134090e+01 4.617509e+00 9.582294e-01 3.514690e+00 
##           78           82           85           98          107          128 
## 1.111482e+00 5.322964e+02 1.920345e+02 3.514690e+00 2.509666e+01 0.000000e+00 
##          132          133          134          143          144          169 
## 3.359815e-01 1.313748e-01 5.684126e+02 2.735390e-01 1.134090e+01 2.509666e+01 
##          182          187          189          203          231          234 
## 2.962600e+00 5.416662e-01 3.514690e+00 4.617509e+00 4.617509e+00 2.509666e+01 
##          246          254          257          258          281          306 
## 1.111482e+00 5.841984e+03 0.000000e+00 2.481715e+03 3.514690e+00 5.416662e-01 
##          345          349          354          376          393          398 
## 0.000000e+00 0.000000e+00 3.514690e+00 1.104132e+01 1.033604e+00 0.000000e+00 
##          448          456          466          470          471          478 
## 3.514690e+00 3.359815e-01 1.676430e+03 3.514690e+00 9.637984e-01 4.617509e+00 
##          499          519          521          522          529          533 
## 0.000000e+00 1.112814e+01 4.617509e+00 4.748416e+02 4.617509e+00 0.000000e+00 
##          568          595          620          639          648          656 
## 1.188829e+03 2.905002e-01 3.514690e+00 0.000000e+00 1.104132e+01 2.509666e+01 
##          657          679          697          743          771          796 
## 1.136210e+02 5.684126e+02 1.111482e+00 2.735390e-01 4.748416e+02 0.000000e+00 
##          822          837          838          840          841          859 
## 0.000000e+00 2.735390e-01 7.296816e+01 3.514690e+00 3.359815e-01 4.617509e+00 
##          861          873          917          940          946          948 
## 0.000000e+00 0.000000e+00 3.514690e+00 2.500398e+03 0.000000e+00 9.637984e-01 
##          968          973          976          994         1000         1002 
## 6.338504e+02 2.509666e+01 5.416662e-01 3.514690e+00 3.514690e+00 2.962600e+00 
##         1024         1031         1032         1039         1055         1076 
## 2.509666e+01 7.296816e+01 0.000000e+00 2.509666e+01 2.735390e-01 3.514690e+00 
##         1102         1110         1138         1163         1172         1175 
## 2.509666e+01 2.544933e+02 2.509666e+01 4.622072e+03 2.509666e+01 5.684126e+02 
##         1209         1214         1218         1223         1224         1257 
## 4.617509e+00 2.509666e+01 3.514690e+00 2.509666e+01 3.514690e+00 2.509666e+01 
##         1258         1280         1307         1313         1329         1362 
## 5.416662e-01 2.509666e+01 5.992822e+02 2.962600e+00 2.509666e+01 9.582294e-01 
##         1412         1415         1416         1424         1429         1445 
## 3.514690e+00 4.617509e+00 3.514690e+00 4.617509e+00 1.134090e+01 1.104132e+01 
##         1462         1467         1481         1483         1494         1507 
## 1.134090e+01 5.684126e+02 4.617509e+00 7.296816e+01 2.962600e+00 3.514690e+00 
##         1544         1559         1596         1598         1639         1657 
## 4.748416e+02 1.646644e+04 3.514690e+00 1.134090e+01 1.111482e+00 1.313748e-01 
##         1660         1705         1709         1718         1739         1752 
## 3.514690e+00 2.509666e+01 4.617509e+00 9.249953e+02 1.111482e+00 4.617509e+00 
##         1760         1790         1826         1833         1849         1884 
## 1.111482e+00 0.000000e+00 0.000000e+00 3.933553e+03 3.514690e+00 1.111482e+00 
##         1898         1902         1924         1933         1984         1994 
## 4.748416e+02 4.617509e+00 0.000000e+00 2.509666e+01 2.509666e+01 2.509666e+01 
##         2001         2011         2019         2026         2042         2063 
## 0.000000e+00 1.111482e+00 5.416662e-01 3.514690e+00 2.314038e+05 0.000000e+00 
##         2084         2129         2143         2149         2188         2192 
## 3.514690e+00 3.514690e+00 3.514690e+00 3.514690e+00 1.595494e+02 0.000000e+00 
##         2193         2199         2227         2250         2286         2293 
## 3.514690e+00 7.296816e+01 1.188829e+03 0.000000e+00 2.509666e+01 4.617509e+00 
##         2316         2329         2330         2335         2349         2350 
## 5.684126e+02 5.684126e+02 0.000000e+00 1.111482e+00 2.962600e+00 3.514690e+00 
##         2377         2380         2388         2393         2405         2415 
## 1.104132e+01 3.514690e+00 2.509666e+01 1.111482e+00 2.735390e-01 4.617509e+00 
##         2426         2427         2460         2462         2466         2471 
## 4.564174e+03 8.338104e+03 7.296816e+01 3.514690e+00 9.637984e-01 3.514690e+00 
##         2484         2491         2492         2502         2504         2516 
## 2.509666e+01 2.962600e+00 2.509666e+01 2.509666e+01 4.617509e+00 5.416662e-01 
##         2524         2526         2527         2533         2542         2549 
## 1.111482e+00 2.180673e+02 3.514690e+00 0.000000e+00 3.514690e+00 2.509666e+01 
##         2557         2562         2582         2596         2601         2603 
## 0.000000e+00 1.595494e+02 3.359815e-01 1.649925e+03 2.509666e+01 4.617509e+00 
##         2623         2660         2663         2701         2720         2730 
## 1.033604e+00 5.684126e+02 1.213503e+03 1.033604e+00 5.416662e-01 0.000000e+00 
##         2738         2795         2806         2811         2820         2835 
## 0.000000e+00 3.514690e+00 0.000000e+00 3.514690e+00 0.000000e+00 3.514690e+00 
##         2844         2846         2849         2861         2872         2876 
## 3.514690e+00 5.684126e+02 3.514690e+00 1.313748e-01 0.000000e+00 4.617509e+00 
##         2908         2920         2951         2961         2986         2987 
## 2.509666e+01 2.509666e+01 1.104132e+01 1.111482e+00 4.617509e+00 1.033604e+00 
##         3009         3020         3029         3051         3058         3065 
## 5.684126e+02 2.962600e+00 3.514690e+00 2.509666e+01 0.000000e+00 3.514690e+00 
##         3066         3091         3103         3119         3134         3136 
## 2.509666e+01 3.514690e+00 1.033604e+00 3.514690e+00 2.735390e-01 5.416662e-01 
##         3137         3150         3152         3158         3167         3186 
## 9.637984e-01 3.514690e+00 4.970885e+03 8.370871e+02 1.033604e+00 3.514690e+00 
##         3187         3200         3230         3260         3265         3278 
## 4.214785e+02 5.306754e+03 2.509666e+01 0.000000e+00 1.357050e+03 0.000000e+00 
##         3298         3314         3327         3345         3350         3356 
## 3.514690e+00 3.514690e+00 3.514690e+00 3.514690e+00 2.509666e+01 7.251781e+01 
##         3384         3397         3401         3404         3408         3411 
## 3.514690e+00 1.097181e+04 5.416662e-01 1.111482e+00 3.514690e+00 1.111482e+00 
##         3443         3459         3461         3469         3491         3505 
## 3.514690e+00 3.514690e+00 2.905002e-01 4.617509e+00 7.296816e+01 0.000000e+00 
##         3516         3519         3533         3549         3554         3557 
## 4.822009e+03 1.188829e+03 2.509666e+01 5.416662e-01 4.617509e+00 3.514690e+00 
##         3571         3577         3595         3596         3635         3648 
## 2.509666e+01 1.111482e+00 1.111482e+00 4.617509e+00 2.962600e+00 3.514690e+00 
##         3651         3723         3727         3728         3733         3750 
## 4.617509e+00 2.509666e+01 5.552928e+02 4.617509e+00 7.251781e+01 2.509666e+01 
##         3752         3753         3790         3833         3845         3857 
## 4.617509e+00 2.962600e+00 2.509666e+01 3.514690e+00 1.112814e+01 0.000000e+00 
##         3873         3893         3940         3965         3987         3989 
## 7.358650e+03 2.509666e+01 1.111482e+00 1.104132e+01 7.296816e+01 0.000000e+00 
##         4010         4011         4014         4068         4070         4080 
## 5.684126e+02 1.033604e+00 3.514690e+00 6.338504e+02 3.514690e+00 2.905002e-01 
##         4081         4102         4124         4159         4214         4229 
## 3.514690e+00 2.509666e+01 0.000000e+00 2.509666e+01 1.104132e+01 3.514690e+00 
##         4243         4245         4273         4276         4303         4304 
## 3.514690e+00 1.104132e+01 3.514690e+00 0.000000e+00 2.509666e+01 4.617509e+00 
##         4310         4323         4350         4352         4369         4374 
## 2.509666e+01 3.514690e+00 0.000000e+00 0.000000e+00 3.514690e+00 7.251781e+01 
##         4384         4432         4461         4470         4472         4476 
## 2.596233e+03 3.514690e+00 0.000000e+00 0.000000e+00 2.509666e+01 2.509666e+01 
##         4489         4526         4536         4542         4550         4590 
## 2.481715e+03 3.514690e+00 2.509666e+01 0.000000e+00 3.359815e-01 2.502509e+02 
##         4600         4615         4633         4667         4705         4708 
## 2.509666e+01 1.104132e+01 3.514690e+00 3.514690e+00 1.033604e+00 2.509666e+01 
##         4730         4750         4751         4756         4760         4792 
## 5.684126e+02 2.509666e+01 7.251781e+01 7.251781e+01 3.514690e+00 4.617509e+00 
##         4800         4801         4820         4822         4823         4833 
## 1.966330e-01 5.416662e-01 4.617509e+00 2.509666e+01 3.359815e-01 2.509666e+01 
##         4843         4846         4862         4864         4875         4879 
## 2.544933e+02 2.509666e+01 1.033604e+00 3.514690e+00 7.251781e+01 0.000000e+00 
##         4890         4904         4910         4921         4930         4954 
## 0.000000e+00 7.296816e+01 3.514690e+00 4.617509e+00 1.233139e+02 7.296816e+01 
##         4964         4982         5014         5015         5044         5049 
## 7.251781e+01 7.296816e+01 1.134090e+01 2.509666e+01 1.033604e+00 5.684126e+02 
##         5055         5057         5072         5103         5115         5120 
## 2.180673e+02 3.514690e+00 3.514690e+00 0.000000e+00 4.748416e+02 4.146368e+04 
##         5132         5136         5146         5179         5189         5223 
## 2.905002e-01 9.358170e+01 1.111482e+00 2.509666e+01 1.111482e+00 3.514690e+00 
##         5231         5251         5292         5293         5327         5331 
## 2.509666e+01 1.104132e+01 1.104132e+01 2.509666e+01 2.509666e+01 0.000000e+00 
##         5342         5359         5423         5424         5438         5446 
## 3.514690e+00 7.296816e+01 3.514690e+00 7.296816e+01 3.514690e+00 1.111482e+00 
##         5453         5461         5466         5507         5508         5531 
## 4.617509e+00 1.966330e-01 7.861847e+03 2.180673e+02 7.870801e+02 3.514690e+00 
##         5547         5552         5554         5556         5564         5579 
## 2.509666e+01 1.676430e+03 0.000000e+00 3.514690e+00 5.416662e-01 0.000000e+00 
##         5583         5597         5624         5666         5670         5688 
## 3.514690e+00 7.251781e+01 2.509666e+01 2.509666e+01 2.509666e+01 2.509666e+01 
##         5707         5714         5726         5731         5771         5793 
## 2.509666e+01 5.684126e+02 3.514690e+00 0.000000e+00 3.514690e+00 2.509666e+01 
##         5846         5849         5867         5881         5886         5899 
## 5.684126e+02 3.514690e+00 2.509666e+01 2.509666e+01 9.637984e-01 1.111482e+00 
##         5901         5902         5904         5905         5906         5911 
## 2.509666e+01 2.509666e+01 2.509666e+01 9.637984e-01 3.514690e+00 4.617509e+00 
##         5912         5918         5920         5939         5948         5962 
## 0.000000e+00 2.509666e+01 5.684126e+02 1.033604e+00 1.111482e+00 2.481715e+03 
##         5965         5973         5994         5996         5999         6003 
## 3.514690e+00 3.514690e+00 2.509666e+01 9.351431e+03 1.033604e+00 2.509666e+01 
##         6009         6018         6022         6054         6078         6085 
## 2.544933e+02 2.596233e+03 7.296816e+01 2.008817e+03 1.582054e+02 2.509666e+01 
##         6118         6121         6125         6134         6145         6163 
## 3.514690e+00 3.514690e+00 4.617509e+00 5.416662e-01 7.251781e+01 3.514690e+00 
##         6169         6173         6190         6202         6221         6223 
## 5.416662e-01 1.112814e+01 2.509666e+01 2.905002e-01 0.000000e+00 3.514690e+00 
##         6258         6322         6336         6345         6349         6350 
## 3.514690e+00 0.000000e+00 1.111482e+00 8.405205e-01 7.296816e+01 5.416662e-01 
##         6354         6367         6370         6373         6391         6404 
## 0.000000e+00 2.509666e+01 2.509666e+01 9.637984e-01 2.509666e+01 0.000000e+00 
##         6451         6472         6498         6505         6554         6563 
## 3.514690e+00 2.509666e+01 2.509666e+01 3.514690e+00 3.514690e+00 0.000000e+00 
##         6576         6591         6600         6630         6647         6679 
## 4.617509e+00 2.481715e+03 1.104132e+01 3.933553e+03 8.405205e-01 2.509666e+01 
##         6690         6695         6742         6757         6764         6784 
## 5.416662e-01 2.509666e+01 3.514690e+00 3.514690e+00 0.000000e+00 2.481715e+03 
##         6785         6815         6821         6857         6860         6869 
## 2.509666e+01 4.665614e+03 3.514690e+00 7.296816e+01 3.514690e+00 5.684126e+02 
##         6876         6880         6901         6914         6918         6920 
## 8.405205e-01 4.622072e+03 0.000000e+00 2.071896e-01 0.000000e+00 3.514690e+00 
##         6938         6939         6943         6946         6949         6955 
## 2.509666e+01 9.582294e-01 2.509666e+01 2.509666e+01 3.514690e+00 4.617509e+00 
##         6962         7026         7041         7048         7082         7103 
## 2.481715e+03 3.514690e+00 0.000000e+00 3.514690e+00 3.514690e+00 3.514690e+00 
##         7109         7116         7129         7137         7194         7202 
## 5.416662e-01 1.033604e+00 3.514690e+00 1.111482e+00 2.509666e+01 3.514690e+00 
##         7242         7261         7277         7295         7313         7316 
## 3.514690e+00 2.509666e+01 8.405205e-01 9.637984e-01 0.000000e+00 2.509666e+01 
##         7335         7337         7345         7352         7367         7373 
## 2.509666e+01 2.735390e-01 1.033604e+00 2.509666e+01 3.514690e+00 4.748416e+02 
##         7375         7392         7397         7398         7401         7430 
## 3.514690e+00 3.514690e+00 1.033604e+00 2.509666e+01 0.000000e+00 1.104132e+01 
##         7456         7458         7461         7472         7480         7482 
## 0.000000e+00 7.296816e+01 4.617509e+00 0.000000e+00 3.514690e+00 2.509666e+01 
##         7483         7508         7514         7564         7566         7569 
## 6.829105e+03 2.509666e+01 3.514690e+00 1.134090e+01 4.617509e+00 1.846896e+04 
##         7578         7619         7623         7624         7649         7697 
## 2.509666e+01 3.514690e+00 3.514690e+00 2.596233e+03 1.111482e+00 0.000000e+00 
##         7718         7731         7746         7756         7762         7765 
## 2.509666e+01 2.509666e+01 7.296816e+01 4.748416e+02 0.000000e+00 4.617509e+00 
##         7772         7779         7825         7830         7837         7850 
## 3.218147e+02 3.514690e+00 7.251781e+01 1.033604e+00 4.617509e+00 1.111482e+00 
##         7859         7862         7887         7890         7902         7904 
## 7.296816e+01 7.251781e+01 2.509666e+01 1.111482e+00 2.962600e+00 3.514690e+00 
##         7905         7941         7962         7964         7966         7983 
## 2.509666e+01 2.509666e+01 1.104132e+01 0.000000e+00 4.617509e+00 2.509666e+01 
##         8006         8015         8030         8077         8113         8123 
## 0.000000e+00 2.509666e+01 7.251781e+01 2.509666e+01 2.509666e+01 5.684126e+02 
##         8133         8134         8168         8174         8181         8183 
## 4.617509e+00 1.637644e+04 7.296816e+01 2.962600e+00 5.416662e-01 2.509666e+01 
##         8208         8220         8223         8253         8267         8293 
## 2.509666e+01 3.514690e+00 3.514690e+00 7.296816e+01 7.104577e+02 2.509666e+01 
##         8294         8309         8338         8342         8362         8365 
## 3.514690e+00 2.015970e+04 4.617509e+00 2.509666e+01 1.033604e+00 5.416662e-01 
##         8370         8373         8382         8393         8413         8426 
## 1.582054e+02 4.617509e+00 2.509666e+01 9.637984e-01 0.000000e+00 4.617509e+00 
##         8485         8542         8546         8566         8593         8609 
## 3.514690e+00 2.509666e+01 3.514690e+00 4.617509e+00 3.514690e+00 4.748416e+02 
##         8627         8663         8679         8708         8742         8746 
## 2.905002e-01 1.104132e+01 5.416662e-01 7.251781e+01 0.000000e+00 2.962600e+00 
##         8751         8761         8783         8787         8798         8825 
## 1.676430e+03 2.509666e+01 9.637984e-01 9.637984e-01 2.509666e+01 4.617509e+00 
##         8831         8850         8868         8878         8880         8894 
## 2.509666e+01 0.000000e+00 3.514690e+00 5.552928e+02 6.735139e+02 4.617509e+00 
##         8914         8931         8939         8953         8957         8992 
## 7.296816e+01 2.509666e+01 7.296816e+01 0.000000e+00 9.637984e-01 5.684126e+02 
##         8997         9015         9018         9025         9048         9061 
## 4.617509e+00 3.514690e+00 0.000000e+00 3.514690e+00 2.962600e+00 9.637984e-01 
##         9095         9098         9117         9129         9140         9163 
## 2.509666e+01 3.933553e+03 2.509666e+01 9.186297e+03 4.185553e+02 1.033604e+00 
##         9204         9210         9228         9229         9250         9253 
## 3.514690e+00 3.514690e+00 2.509666e+01 2.509666e+01 6.735139e+02 4.617509e+00 
##         9309         9310         9320         9341         9350         9355 
## 1.104132e+01 3.514690e+00 1.112814e+01 3.514690e+00 4.617509e+00 3.514690e+00 
##         9358         9373         9384         9407         9413         9424 
## 2.292348e+02 0.000000e+00 1.104132e+01 1.111482e+00 7.296816e+01 2.509666e+01 
##         9481         9486         9500         9553         9568         9570 
## 9.637984e-01 0.000000e+00 0.000000e+00 2.962600e+00 2.509666e+01 1.111482e+00 
##         9596         9607         9619         9641         9652         9659 
## 5.416662e-01 0.000000e+00 2.509666e+01 1.111482e+00 2.962600e+00 1.357050e+03 
##         9661         9664         9679         9682         9684         9714 
## 3.514690e+00 1.033604e+00 1.582054e+02 3.514690e+00 2.509666e+01 0.000000e+00 
##         9726         9763         9766         9782         9785         9792 
## 3.230174e+03 3.230174e+03 5.416662e-01 1.613997e-02 3.514690e+00 1.111482e+00 
##         9794         9809         9816         9834         9848         9851 
## 3.514690e+00 5.416662e-01 2.509666e+01 2.509666e+01 1.637644e+04 1.033604e+00 
##         9857         9877         9895         9905         9920        10003 
## 1.785714e-02 3.514690e+00 1.613997e-02 2.509666e+01 5.416662e-01 2.509666e+01 
##        10012        10054        10105        10110        10117        10118 
## 2.509666e+01 3.086590e+03 2.282577e+03 7.251781e+01 0.000000e+00 1.613997e-02 
##        10130        10155        10178        10201        10206        10209 
## 3.514690e+00 3.514690e+00 2.544933e+02 3.514690e+00 7.132508e+03 3.514690e+00 
##        10212        10241        10262        10270        10279        10290 
## 3.359815e-01 9.186297e+03 5.416662e-01 3.514690e+00 7.296816e+01 2.509666e+01 
##        10303        10364        10371        10386        10404        10423 
## 2.509666e+01 2.481715e+03 3.514690e+00 4.680233e+03 4.281273e+02 1.111482e+00 
##        10439        10449        10475        10480        10487        10500 
## 2.509666e+01 4.617509e+00 1.314655e-01 1.111482e+00 2.509666e+01 3.514690e+00 
##        10512        10516        10527        10544        10549        10568 
## 9.637984e-01 1.104132e+01 3.514690e+00 4.617509e+00 2.509666e+01 4.617509e+00 
##        10572        10582        10590        10638        10650        10694 
## 2.509666e+01 1.111482e+00 4.617509e+00 3.898724e+04 7.964028e+02 1.104132e+01 
##        10708        10724        10730        10736        10759        10771 
## 2.735390e-01 7.296816e+01 3.514690e+00 2.509666e+01 3.514690e+00 9.637984e-01 
##        10774        10776        10782        10802        10808        10836 
## 3.514690e+00 1.033604e+00 0.000000e+00 3.514690e+00 2.509666e+01 1.313748e-01 
##        10862        10874        10882        10886        10891        10906 
## 3.514690e+00 2.962600e+00 4.617509e+00 0.000000e+00 5.552928e+02 3.514690e+00 
##        10920        10929        10944        10952        10974        10995 
## 4.617509e+00 3.514690e+00 3.514690e+00 5.416662e-01 5.684126e+02 2.509666e+01 
##        11011        11025        11044        11073        11074        11123 
## 5.416662e-01 2.509666e+01 9.637984e-01 1.966330e-01 4.617509e+00 1.033604e+00 
##        11132        11142        11146        11156        11164        11171 
## 0.000000e+00 1.033604e+00 3.514690e+00 1.134090e+01 0.000000e+00 1.134090e+01 
##        11178        11217        11225        11234        11257        11296 
## 1.111482e+00 2.509666e+01 3.514690e+00 7.938586e+03 3.514690e+00 2.509666e+01 
##        11302        11305        11342        11352        11388        11390 
## 2.735390e-01 1.111482e+00 1.476768e+03 7.296816e+01 7.251781e+01 3.514690e+00 
##        11396        11417        11443        11456        11457        11461 
## 0.000000e+00 2.509666e+01 1.104132e+01 8.405205e-01 3.359815e-01 0.000000e+00 
##        11504        11527        11559        11560        11592        11606 
## 5.416662e-01 0.000000e+00 4.617509e+00 2.509666e+01 2.962600e+00 3.514690e+00 
##        11608        11642        11664        11671        11678        11700 
## 3.661025e+04 3.514690e+00 0.000000e+00 2.509666e+01 1.111482e+00 3.514690e+00 
##        11704        11707        11728        11729        11735        11753 
## 3.514690e+00 3.933553e+03 2.180673e+02 1.112814e+01 5.684126e+02 1.033604e+00 
##        11757        11818        11820        11839        11843        11859 
## 3.514690e+00 0.000000e+00 1.111482e+00 0.000000e+00 7.251781e+01 4.617509e+00 
##        11862        11887        11896        11935        11980        11988 
## 0.000000e+00 3.272829e+03 2.509666e+01 3.514690e+00 2.735390e-01 3.514690e+00 
##        12016        12030        12032        12049        12051        12075 
## 4.617509e+00 3.514690e+00 2.509666e+01 4.617509e+00 7.251781e+01 2.509666e+01 
##        12084        12091        12109        12114        12117        12128 
## 2.509666e+01 3.514690e+00 8.840404e+03 0.000000e+00 7.296816e+01 0.000000e+00 
##        12147        12160        12166        12190        12216        12236 
## 5.684126e+02 0.000000e+00 1.313748e-01 2.509666e+01 5.684126e+02 4.617509e+00 
##        12283        12307        12335        12367        12372        12376 
## 2.962600e+00 7.251781e+01 5.684126e+02 2.509666e+01 0.000000e+00 2.509666e+01 
##        12380        12382        12389        12395        12397        12408 
## 4.617509e+00 7.296816e+01 2.962600e+00 2.962600e+00 4.617509e+00 3.514690e+00 
##        12427        12439        12450        12452        12465        12468 
## 2.509666e+01 8.405205e-01 0.000000e+00 0.000000e+00 3.514690e+00 1.111482e+00 
##        12490        12496        12522        12527        12528        12537 
## 4.617509e+00 4.617509e+00 5.416662e-01 1.033604e+00 3.514690e+00 3.514690e+00 
##        12546        12550        12552        12554        12561        12568 
## 5.416662e-01 2.509666e+01 2.509666e+01 2.735390e-01 4.281273e+02 2.509666e+01 
##        12570        12579        12593        12607        12609        12622 
## 3.514690e+00 3.514690e+00 1.104132e+01 3.514690e+00 2.509666e+01 7.296816e+01 
##        12648        12705        12707        12739        12751        12761 
## 2.509666e+01 0.000000e+00 5.684126e+02 1.112814e+01 0.000000e+00 4.348904e+03 
##        12782        12799        12804        12806        12816        12843 
## 0.000000e+00 3.514690e+00 5.416662e-01 3.514690e+00 2.905002e-01 7.296816e+01 
##        12887        12888        12894        12901        12906        12918 
## 3.514690e+00 3.514690e+00 2.509666e+01 4.622072e+03 3.514690e+00 7.296816e+01 
##        12933        12943        12948        12956        12964        12968 
## 1.684093e+03 1.033604e+00 3.230174e+03 2.544933e+02 0.000000e+00 3.514690e+00 
##        12980        12984        13000        13035        13052        13087 
## 2.509666e+01 3.514690e+00 5.684126e+02 3.514690e+00 0.000000e+00 4.748416e+02 
##        13092        13104        13111        13133        13136        13137 
## 2.509666e+01 2.509666e+01 4.617509e+00 2.509666e+01 3.218147e+02 0.000000e+00 
##        13138        13143        13150        13154        13159        13188 
## 2.735390e-01 3.514690e+00 9.637984e-01 1.111482e+00 2.509666e+01 3.514690e+00 
##        13252        13261        13263        13284        13335        13336 
## 3.514690e+00 2.509666e+01 1.966330e-01 1.111482e+00 1.111482e+00 3.514690e+00 
##        13341        13360        13396        13450        13469        13497 
## 2.509666e+01 4.617509e+00 3.514690e+00 3.514690e+00 2.905002e-01 1.111482e+00 
##        13540        13553        13565        13586        13602        13621 
## 2.282577e+03 2.509666e+01 2.735390e-01 5.416662e-01 4.617509e+00 1.111482e+00 
##        13635        13636        13647        13656        13660        13674 
## 3.359815e-01 9.637984e-01 3.514690e+00 1.111482e+00 7.296816e+01 3.514690e+00 
##        13675        13682        13690        13732        13737        13742 
## 3.514690e+00 0.000000e+00 1.111482e+00 3.514690e+00 7.251781e+01 4.617509e+00 
##        13753        13755        13761        13777        13778        13782 
## 3.514690e+00 2.509666e+01 2.509666e+01 8.146378e+03 2.735390e-01 4.617509e+00 
##        13784        13791        13807        13892        13916        13962 
## 2.509666e+01 0.000000e+00 3.514690e+00 3.514690e+00 2.071896e-01 3.514690e+00 
##        13967        13989        14009        14035        14037        14060 
## 2.509666e+01 2.509666e+01 1.033604e+00 3.514690e+00 2.509666e+01 2.509666e+01 
##        14061        14064        14085        14095        14104        14110 
## 2.962600e+00 8.405205e-01 3.514690e+00 4.617509e+00 0.000000e+00 5.416662e-01 
##        14118        14119        14122        14125        14135        14137 
## 1.111482e+00 1.188829e+03 3.514690e+00 3.514690e+00 3.514690e+00 2.509666e+01 
##        14158        14187        14203        14204        14210        14216 
## 5.416662e-01 2.509666e+01 4.617509e+00 1.044062e+02 3.514690e+00 7.251781e+01 
##        14221        14256        14305        14311        14318        14321 
## 5.416662e-01 1.313748e-01 3.514690e+00 2.198806e+03 3.514690e+00 2.509666e+01 
##        14346        14358        14362        14368        14374        14403 
## 3.540056e+04 4.617509e+00 2.509666e+01 2.509666e+01 0.000000e+00 2.509666e+01 
##        14404        14414        14422        14435        14443        14481 
## 1.561911e+05 2.509666e+01 3.514690e+00 3.514690e+00 7.296816e+01 0.000000e+00 
##        14543        14571        14581        14592        14609        14628 
## 3.514690e+00 1.613997e-02 2.962600e+00 3.514690e+00 0.000000e+00 3.514690e+00 
##        14633        14635        14664        14683        14692        14725 
## 7.296816e+01 4.617509e+00 3.514690e+00 0.000000e+00 4.617509e+00 2.509666e+01 
##        14741        14743        14747        14751        14762        14780 
## 2.509666e+01 3.514690e+00 2.509666e+01 3.514690e+00 5.684126e+02 2.509666e+01 
##        14781        14787        14817        14819        14860        14895 
## 1.308141e+02 3.514690e+00 0.000000e+00 2.509666e+01 0.000000e+00 5.416662e-01 
##        14907        14925        14945        14947        14955        14963 
## 3.514690e+00 2.509666e+01 3.514690e+00 1.104132e+01 1.111482e+00 8.962168e+02 
##        15005        15024        15037        15096        15134        15143 
## 1.622603e+03 2.509666e+01 2.509666e+01 3.514690e+00 5.416662e-01 3.218147e+02 
##        15194        15196        15200        15217        15220        15242 
## 4.617509e+00 7.296816e+01 5.416662e-01 1.582054e+02 1.111482e+00 7.251781e+01 
##        15249 
## 3.514690e+00
hist(betweenness_centrality, labels = TRUE, ylim = c(0,2000), xlim = c(0,250000), xlab = "Betweenness Centrality", main = "Histograma de los Valores de Betweenness Centrality")

Graficamos a continuación la red de usuarios-usuarios donde cada nodo tiene el tamaño y color asociado a la métrica de betweenness calculada anteriormente.

colorfunc <- colorRampPalette(c( "red",
                                 "firebrick",
                                 "lightcoral",
                                 "saddlebrown",
                                 "tomato", 
                                 "darkorange",
                                 "gold", 
                                 "lightgreen",
                                 "mediumspringgreen",
                                 "dodgerblue",
                                 "steelblue"))
scaled_betweenness = (betweenness_centrality/1000) +1
colors <- colorfunc(max(scaled_betweenness))
V(users_projected)$color <- colors[scaled_betweenness]
V(users_projected)$shape <- "circle"
E(users_projected)$color <- "lightgray"

plot(users_projected, 
     vertex.label = NA,
     vertex.size =  scaled_betweenness,
     edge.arrow.size=0.1,
     layout = layout_nicely,
     main = "Proyeccion Red Usuarios- Nodos Según el Betweenness")

Medidas Sobre Conjuntos de Nodos

Cliques

Cálculo de la distribución de cliques:

count_max_cliques(users_projected)
## [1] 79

La red contiene 79 cliques.

¿Cuál es el tamaño de cada clique?

total_cliques = max_cliques(users_projected) 
cliques_sizes = unlist(lapply(total_cliques, length))
h = hist(cliques_sizes, 
         ylim=c(0,80),
         breaks = 5,
         xlab = "Tamaño de los cliques", 
         ylab = "Frecuencia", 
         main = "Distribución del tamaño de los cliques" ) 

text(h$mids,h$counts,labels=h$counts, adj=c(0.5, -0.5))

Graficamos el clique más grande:

largestCliques <- largest_cliques(users_projected)

largestClique_1 = largestCliques[[1]]
g_induced = induced_subgraph(users_projected, largestClique_1)
V(g_induced)$color <- "lightblue"

plot(g_induced,
     vertex.label = NA,
     layout=layout_components,
     edge.arrow.size=0.05,
     vertex.size = 10)

Medidas Globales

Radio

Calculado obteniendo el mínimo valor de eccentricity

eccentricity_metric = eccentricity(users_projected)
min(eccentricity_metric)
## [1] 3

Diametro

diameter_metric = diameter(users_projected)
diameter_metric
## [1] 6

Average Path Length

avg_path_length = mean_distance(users_projected, directed=F)
avg_path_length
## [1] 2.658437

Clustering Promedio

clustering_avg = transitivity(users_projected, type = "average")
clustering_avg
## [1] 0.9563615

Coeficiente de Reciprocidad

reciprocity(users_projected)
## [1] 1

Subredes

K-Core

La función coreness nos da una tabla indicando que core pertenece a cada nodo:

coreness(users_projected)
##    10    11    41    51   114    67    78    82    85    98   107   128   132 
##   220    81    28   126    14   253    67    81     3   253   220    18    12 
##   133   134   143   144   169   182   187   189   203   231   234   246   254 
##    11   253    21    28   220    62    52   253   126   126   220    67    81 
##   257   258   281   306   345   349   354   376   393   398   448   456   466 
##    81   220   253    52    81    81   253    44    48    81   253    12   220 
##   470   471   478   499   519   521   522   529   533   568   595   620   639 
##   253    30   126    81    25   126   126   126    81   220    14   253    81 
##   648   656   657   679   697   743   771   796   822   837   838   840   841 
##    44   220    44   253    67    21   126    81    81    21    46   253    12 
##   859   861   873   917   940   946   948   968   973   976   994  1000  1002 
##   126    81    81   253   126    81    30    62   220    52   253   253    62 
##  1024  1031  1032  1039  1055  1076  1102  1110  1138  1163  1172  1175  1209 
##   220    46    18   220    21   253   220   126   220   220   220   253   126 
##  1214  1218  1223  1224  1257  1258  1280  1307  1313  1329  1362  1412  1415 
##   220   253   220   253   220    52   220    48    62   220    14   253   126 
##  1416  1424  1429  1445  1462  1467  1481  1483  1494  1507  1544  1559  1596 
##   253   126    28    44    28   253   126    46    62   253   126   126   253 
##  1598  1639  1657  1660  1705  1709  1718  1739  1752  1760  1790  1826  1833 
##    28    67    11   253   220   126    14    67   126    67    81     4   253 
##  1849  1884  1898  1902  1924  1933  1984  1994  2001  2011  2019  2026  2042 
##   253    67   126   126    81   220   220   220    81    67    52   253   220 
##  2063  2084  2129  2143  2149  2188  2192  2193  2199  2227  2250  2286  2293 
##    18   253   253   253   253   126    81   253    46   220    18   220   126 
##  2316  2329  2330  2335  2349  2350  2377  2380  2388  2393  2405  2415  2426 
##   253   253    81    67    62   253    44   253   220    67    21   126   253 
##  2427  2460  2462  2466  2471  2484  2491  2492  2502  2504  2516  2524  2526 
##   253    46   253    30   253   220    62   220   220   126    52    67    52 
##  2527  2533  2542  2549  2557  2562  2582  2596  2601  2603  2623  2660  2663 
##   253     5   253   220    18   126    12   126   220   126    48   253    62 
##  2701  2720  2730  2738  2795  2806  2811  2820  2835  2844  2846  2849  2861 
##    48    52    81    81   253     3   253     2   253   253   253   253    11 
##  2872  2876  2908  2920  2951  2961  2986  2987  3009  3020  3029  3051  3058 
##     3   126   220   220    44    67   126    48   253    62   253   220    81 
##  3065  3066  3091  3103  3119  3134  3136  3137  3150  3152  3158  3167  3186 
##   253   220   253    48   253    21    52    30   253    67   126    48   253 
##  3187  3200  3230  3260  3265  3278  3298  3314  3327  3345  3350  3356  3384 
##   126   253   220     2   253    81   253   253   253   253   220    31   253 
##  3397  3401  3404  3408  3411  3443  3459  3461  3469  3491  3505  3516  3519 
##   126    52    67   253    67   253   253    14   126    46    81   253   220 
##  3533  3549  3554  3557  3571  3577  3595  3596  3635  3648  3651  3723  3727 
##   220    52   126   253   220    67    67   126    62   253   126   220    67 
##  3728  3733  3750  3752  3753  3790  3833  3845  3857  3873  3893  3940  3965 
##   126    31   220   126    62   220   253    25    81    81   220    67    44 
##  3987  3989  4010  4011  4014  4068  4070  4080  4081  4102  4124  4159  4214 
##    46    81   253    48   253    62   253    14   253   220    18   220    44 
##  4229  4243  4245  4273  4276  4303  4304  4310  4323  4350  4352  4369  4374 
##   253   253    44   253    81   220   126   220   253     2     5   253    31 
##  4384  4432  4461  4470  4472  4476  4489  4526  4536  4542  4550  4590  4600 
##   220   253    18    81   220   220   220   253   220    81    12    21   220 
##  4615  4633  4667  4705  4708  4730  4750  4751  4756  4760  4792  4800  4801 
##    44   253   253    48   220   253   220    31    31   253   126    11    52 
##  4820  4822  4823  4833  4843  4846  4862  4864  4875  4879  4890  4904  4910 
##   126   220    12   220   126   220    48   253    31    18    81    46   253 
##  4921  4930  4954  4964  4982  5014  5015  5044  5049  5055  5057  5072  5103 
##   126    30    46    31    46    28   220    48   253    52   253   253    18 
##  5115  5120  5132  5136  5146  5179  5189  5223  5231  5251  5292  5293  5327 
##   126   126    14    44    67   220    67   253   220    44    44   220   220 
##  5331  5342  5359  5423  5424  5438  5446  5453  5461  5466  5507  5508  5531 
##    81   253    46   253    46   253    67   126    11   220    52   126   253 
##  5547  5552  5554  5556  5564  5579  5583  5597  5624  5666  5670  5688  5707 
##   220   220    81   253    52     2   253    31   220   220   220   220   220 
##  5714  5726  5731  5771  5793  5846  5849  5867  5881  5886  5899  5901  5902 
##   253   253    81   253   220   253   253   220   220    30    67   220   220 
##  5904  5905  5906  5911  5912  5918  5920  5939  5948  5962  5965  5973  5994 
##   220    30   253   126    81   220   253    48    67   220   253   253   220 
##  5996  5999  6003  6009  6018  6022  6054  6078  6085  6118  6121  6125  6134 
##   253    48   220   126   220    46   126    46   220   253   253   126    52 
##  6145  6163  6169  6173  6190  6202  6221  6223  6258  6322  6336  6345  6349 
##    31   253    52    25   220    14    81   253   253    81    67    21    46 
##  6350  6354  6367  6370  6373  6391  6404  6451  6472  6498  6505  6554  6563 
##    52    81   220   220    30   220    81   253   220   220   253   253    81 
##  6576  6591  6600  6630  6647  6679  6690  6695  6742  6757  6764  6784  6785 
##   126   220    44   253    21   220    52   220   253   253    81   220   220 
##  6815  6821  6857  6860  6869  6876  6880  6901  6914  6918  6920  6938  6939 
##   253   253    46   253   253    21   220    81     5     3   253   220    14 
##  6943  6946  6949  6955  6962  7026  7041  7048  7082  7103  7109  7116  7129 
##   220   220   253   126   220   253    81   253   253   253    52    48   253 
##  7137  7194  7202  7242  7261  7277  7295  7313  7316  7335  7337  7345  7352 
##    67   220   253   253   220    21    30    81   220   220    21    48   220 
##  7367  7373  7375  7392  7397  7398  7401  7430  7456  7458  7461  7472  7480 
##   253   126   253   253    48   220    81    44    81    46   126    18   253 
##  7482  7483  7508  7514  7564  7566  7569  7578  7619  7623  7624  7649  7697 
##   220   220   220   253    28   126    30   220   253   253   220    67    81 
##  7718  7731  7746  7756  7762  7765  7772  7779  7825  7830  7837  7850  7859 
##   220   220    46   126     4   126   126   253    31    48   126    67    46 
##  7862  7887  7890  7902  7904  7905  7941  7962  7964  7966  7983  8006  8015 
##    31   220    67    62   253   220   220    44    81   126   220    81   220 
##  8030  8077  8113  8123  8133  8134  8168  8174  8181  8183  8208  8220  8223 
##    31   220   220   253   126   126    46    62    52   220   220   253   253 
##  8253  8267  8293  8294  8309  8338  8342  8362  8365  8370  8373  8382  8393 
##    46    52   220   253    81   126   220    48    52    46   126   220    30 
##  8413  8426  8485  8542  8546  8566  8593  8609  8627  8663  8679  8708  8742 
##    81   126   253   220   253   126   253   126    14    44    52    31    81 
##  8746  8751  8761  8783  8787  8798  8825  8831  8850  8868  8878  8880  8894 
##    62   220   220    30    30   220   126   220    81   253    67   126   126 
##  8914  8931  8939  8953  8957  8992  8997  9015  9018  9025  9048  9061  9095 
##    46   220    46    81    30   253   126   253     2   253    62    30   220 
##  9098  9117  9129  9140  9163  9204  9210  9228  9229  9250  9253  9309  9310 
##   253   220   220   126    48   253   253   220   220   126   126    44   253 
##  9320  9341  9350  9355  9358  9373  9384  9407  9413  9424  9481  9486  9500 
##    25   253   126   253    48    81    44    67    46   220    30    81    81 
##  9553  9568  9570  9596  9607  9619  9641  9652  9659  9661  9664  9679  9682 
##    62   220    67    52     5   220    67    62   253   253    48    46   253 
##  9684  9714  9726  9763  9766  9782  9785  9792  9794  9809  9816  9834  9848 
##   220    18   220   220    52     6   253    67   253    52   220   220   126 
##  9851  9857  9877  9895  9905  9920 10003 10012 10054 10105 10110 10117 10118 
##    48     2   253     6   220    52   220   220   126   220    31    81     6 
## 10130 10155 10178 10201 10206 10209 10212 10241 10262 10270 10279 10290 10303 
##   253   253   126   253   220   253    12   220    52   253    46   220   220 
## 10364 10371 10386 10404 10423 10439 10449 10475 10480 10487 10500 10512 10516 
##   220   253   220   126    67   220   126     2    67   220   253    30    44 
## 10527 10544 10549 10568 10572 10582 10590 10638 10650 10694 10708 10724 10730 
##   253   126   220   126   220    67   126   220   253    44    21    46   253 
## 10736 10759 10771 10774 10776 10782 10802 10808 10836 10862 10874 10882 10886 
##   220   253    30   253    48    81   253   220    11   253    62   126    18 
## 10891 10906 10920 10929 10944 10952 10974 10995 11011 11025 11044 11073 11074 
##    67   253   126   253   253    52   253   220    52   220    30    11   126 
## 11123 11132 11142 11146 11156 11164 11171 11178 11217 11225 11234 11257 11296 
##    48    81    48   253    28     3    28    67   220   253   253   253   220 
## 11302 11305 11342 11352 11388 11390 11396 11417 11443 11456 11457 11461 11504 
##    21    67    67    46    31   253    18   220    44    21    12     3    52 
## 11527 11559 11560 11592 11606 11608 11642 11664 11671 11678 11700 11704 11707 
##    81   126   220    62   253   126   253    81   220    67   253   253   253 
## 11728 11729 11735 11753 11757 11818 11820 11839 11843 11859 11862 11887 11896 
##    52    25   253    48   253    81    67    81    31   126    81   220   220 
## 11935 11980 11988 12016 12030 12032 12049 12051 12075 12084 12091 12109 12114 
##   253    21   253   126   253   220   126    31   220   220   253   220    81 
## 12117 12128 12147 12160 12166 12190 12216 12236 12283 12307 12335 12367 12372 
##    46    18   253    81    11   220   253   126    62    31   253   220    18 
## 12376 12380 12382 12389 12395 12397 12408 12427 12439 12450 12452 12465 12468 
##   220   126    46    62    62   126   253   220    21    81    81   253    67 
## 12490 12496 12522 12527 12528 12537 12546 12550 12552 12554 12561 12568 12570 
##   126   126    52    48   253   253    52   220   220    21   126   220   253 
## 12579 12593 12607 12609 12622 12648 12705 12707 12739 12751 12761 12782 12799 
##   253    44   253   220    46   220    81   253    25    81    11    81   253 
## 12804 12806 12816 12843 12887 12888 12894 12901 12906 12918 12933 12943 12948 
##    52   253    14    46   253   253   220   220   253    46    67    48   220 
## 12956 12964 12968 12980 12984 13000 13035 13052 13087 13092 13104 13111 13133 
##   126    81   253   220   253   253   253    81   126   220   220   126   220 
## 13136 13137 13138 13143 13150 13154 13159 13188 13252 13261 13263 13284 13335 
##   126    81    21   253    30    67   220   253   253   220    11    67    67 
## 13336 13341 13360 13396 13450 13469 13497 13540 13553 13565 13586 13602 13621 
##   253   220   126   253   253    14    67   220   220    21    52   126    67 
## 13635 13636 13647 13656 13660 13674 13675 13682 13690 13732 13737 13742 13753 
##    12    30   253    67    46   253   253    81    67   253    31   126   253 
## 13755 13761 13777 13778 13782 13784 13791 13807 13892 13916 13962 13967 13989 
##   220   220   220    21   126   220    81   253   253     5   253   220   220 
## 14009 14035 14037 14060 14061 14064 14085 14095 14104 14110 14118 14119 14122 
##    48   253   220   220    62    21   253   126    18    52    67   220   253 
## 14125 14135 14137 14158 14187 14203 14204 14210 14216 14221 14256 14305 14311 
##   253   253   220    52   220   126    67   253    31    52    11   253    21 
## 14318 14321 14346 14358 14362 14368 14374 14403 14404 14414 14422 14435 14443 
##   253   220   126   126   220   220    81   220   253   220   253   253    46 
## 14481 14543 14571 14581 14592 14609 14628 14633 14635 14664 14683 14692 14725 
##    81   253     6    62   253     2   253    46   126   253    18   126   220 
## 14741 14743 14747 14751 14762 14780 14781 14787 14817 14819 14860 14895 14907 
##   220   253   220   253   253   220     4   253    81   220    18    52   253 
## 14925 14945 14947 14955 14963 15005 15024 15037 15096 15134 15143 15194 15196 
##   220   253    44    67    67   126   220   220   253    52   126   126    46 
## 15200 15217 15220 15242 15249 
##    52    46    67    31   253

En este gráfico podemos observar la red usuarios-usuarios. Cada nodo tiene un atributo asignado que es el K-core obtenido mediante la función de coreness. Además, cada nodo tiene asociado un color en función del valor del k-core. Los nodos con valores más altos, son los nodos que están más densamente conectados.

kcore <- coreness(users_projected)    # Extraemos k-cores
V(users_projected)$core <- kcore      # Agregamos los k-cores calculados como atributo de los nodos

colorfunc <- colorRampPalette(c( "Red 2",
                                 "lightcoral",
                                 "tomato", 
                                 "orange",
                                 "Cadet Blue 1",
                                 "Yellow 3",
                                 "gold", 
                                 "lightgreen",
                                 "Light Steel Blue 2",
                                 "Royal Blue 1",
                                 "Deep Sky Blue 1",
                                 "Slate Blue"))
colors <- colorfunc(max(kcore))
V(users_projected)$color <- colors[kcore]

plot(users_projected, 
     vertex.size = 3,
     layout = layout_components,
     main="Proyeccion Red Usuarios - Nodos Según el Core al que Pertenecen")

plot(users_projected, 
     vertex.label=NA,
     vertex.size = 3,
     layout = layout_components,
     main="Proyeccion Red Usuarios - Nodos Según el Core al que Pertenecen")

egog = make_ego_graph(users_projected, order=2)
k_g = egog[[1]]
degree_k_g = degree(k_g)

colorfunc <- colorRampPalette(c( "Red 2",
                                 "lightcoral",
                                 "tomato", 
                                 "orange",
                                 "Cadet Blue 1",
                                 "Yellow 3",
                                 "gold", 
                                 "lightgreen",
                                 "Light Steel Blue 2",
                                 "Royal Blue 1",
                                 "Deep Sky Blue 1",
                                 "Slate Blue"))
scaled_degree = degree_k_g + 1
colors <- colorfunc(max(scaled_degree))
V(k_g)$color <- colors[scaled_degree]


plot(k_g, 
     vertex.size = 3,
     vertex.label = degree_k_g,
     edge.arrow.size=0.3,
     layout = layout_components,
     main = "Subgrafo Inducido: Nodos Según Degree")

plot(k_g, 
     vertex.size = 3,
     vertex.label = NA,
     edge.arrow.size=0.3,
     layout = layout_components,
     main = "Subgrafo Inducido: Nodos Según Degree")